Direct And Inverse Proportions

Since, u and v vary directly, u.e.

If u = 10 and v = 15, then,

In option (a)

In option (b),

In option (c),

In option (d),

So, option (c) is not a possible pair of corresponding values of u and v.

Hence, option (c) is correct.

Since x and y vary inversely, i.e.

If x = 10 and y = 6

∴

In option (a),

In option (b),

In option (c), 25× 2.4 = 60

In option (d), 45 × 1.3 = 58.3

Hence option (d) is correct.

(a) If land to be uniformly fertile, then the area of land and the yield on it vary directly with each other.

Hence, option (a) is correct.

Note two quantities x and y are said to be in direct proportion, if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.

The number of the teeth and the age of a person vary sometimes directly and sometimes inversely with each other, we cannot predict about the number of teeth with exactly the age of a person. It changes with person-to-person

Hence, option(d) is correct.

A truck need 54L of diesel for covering a distance = 297km

∴ In 1L, the truck can cover the distance =

Thus, for 550 km, the required diesel of truck =

Hence option (a) is correct.

∵ Speed of the car = 48km/h

Time taken by car = 10h

∴ Distance = Speed × time = 48 × 10 = 480km

If car need to cover 480km in 8h, then

Required speed = km/h

Hence, option (a) is correct.

In option (a)

x = .5,2,8,32 and y = 2,8,32,128

if we multiply x with 4, we get the directly required result as same as shown in corresponding y. in this case, as the value of x increase, the value of y also increase. Hence, option(a) is correct.

In option (b),

If we multiply p and q with 1,2,3 and 4, we get the given result. But it is not given inversely.

In option (c),

If we multiply r with 2.5 and s with 2.5, we will get the given result.

In option (d),

If u = 2, then v = 18

If u = 4, then v = 9

If u = 6, then v = 6

If u = 9, then v = 4

And if u = 12, then v = 3

It shows, when u increases, then v decreases.

Hence it is inversely with each other.

We know that, when we increase the speed, then time taken by vehicle decreases.

Hence, speed and time taken vary inversely with each other.

So, option (d) is correct

If both x and y are in directly proportion, then are in inverse proportion.

Hence, option(b) is correct.

Note that two quantities x and y are said to be in inverse proportion, if an increase in x cause a proportional decrease in y and vice-a-versa.

Given, speed of cycle = 12km/h

Time taken by Meenakshi through cycle = 20min

Then, total distance cover = km

If Meenakshi want to reach her school in 12 min, then her cycle speed should be km/h

Hence, option(c) is correct.

∵ 100 persons had food provision for 24 days.

∴ 1 person had food provision for 24 × 100 i.e. 2400 days

If 20 persons left the place, then remaining persons = (100-20) = 80

∴ 80 persons had food provision for

Hence, option (a) is correct.

If two quantities x and y vary directly with each other, then .

Since, in direct proportion, both x and y increases or decreases together such a manner that the ratio of their corresponding value remains constant.

Hence, option (a) is correct

If two quantities p and q vary inversely with each other, then p×q remains constant.

Since, in inverse proportion, an increase in p cause a proportional decrease in q and vice-a-versa.

Hence, option(c) is correct.

The distance travelled by a rickshaw in 1h = 10km

In 1 min, rickshaw covered the distance

= [∵1h = 60min and 1km = 1000m]

=

Hence, option (d) is correct.

Both x and y vary directly with each other.

i.e. x

if x = 10 and y = 14

so, 10 14 or 5 7

This proportion is not follow in option (b) pairs.

Hence, Option(b) is correct.

Given,

Then,

∴ x and y vary directly with each other.

Given, xy = 10

⇒

Hence, a and y vary inversely with each other.

When two quantities x and y are in direct proportion or vary directly, they are written as .

When two quantities x and y are in inverse proportion or vary inversely, they are written as

Both x and y are said to vary inversely with each other, if for some positive number k, xy = k.

x and y are said to vary directly with each other, if for, some positive number k,

Two quantities are said to vary directly with each other if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

Two quantities are said to vary inversely with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant.

∵ 12 pumps can empty a reservoir in 20h.

∴ 1 pump can empty in 20 × 12 i.e. 240h.

Then, 45 pumps can empty the same reservoir in

⇒

⇒

⇒ 5× 60 + 20

⇒ 5h 20min

if x varies inversely as y, then

xy = k(constant) …(1)

if x = 60 and y = 10

∴ xy = 60× 10 = 600

⇒ k = 600

When y = 2, then from Eq. (i)

x × 2 = k

⇒ 2x = 600

⇒ x = 300

if x varies directly as y, then …(i)

If x = 12 and y = 48, then

⇒

When x = 6, then from Eq.(i)

⇒

⇒

⇒ 6×4 = y×1

⇒ y = 24

When the speed remains constant, the distance travelled is directly proportional to the time.

e.g. if 10km cover in 10min with uniform speed, then 20km cover in 20min with same speed.

On increasing a, b increases in such a manner that remains constant and positive, then a and b are said to vary directly with each other.

If on increasing a, b decreases in such a manner that ab remains constant and positive, then a and b are said to vary inversely with each other.

If two quantities x and y vary directly with each other, then ratio of their corresponding values remains constant.

If two quantities p and q vary inversely with each other then product of their corresponding values remains constant.

The perimeter of a circle and its diameter vary directly with each other

Perimeter of a circle = 2� r

Diameter of a circle = 2×r

⇒ π × Diameter

A car travelling in 1h = 48km

So, car travelled in 1min = km

Similarly, car travelled in 12min =

An auto rickshaw takes 3h to cover a distance of 36km.

Then, its speed = km/h

If its speed increases 4km/h, then

New speed = 12 + 4 = 16km/h

Now, time taken by auto rickshaw to cover 36km in

=

= 2h 15 min

The thickness of a pile of 12 cardboard sheets = 45mm

∴ the thickness of a pile of 1 cardboard sheet = mm

So, the thickness of a pile of 240 cardboard sheets

⇒ ⇒

=

X varies inversely as y.

In inverse proportion,

If x = 4 and y = 6, then k = 4×6 = 24

Now, when x = 3, then

⇒

In direct proportion,

⇒

Where,

In inverse proportion,

⇒

⇒ a₂b₁ = a₁b₂

∵ The area occupied by 15 postal stamps = 60cm²

∴the area occupied by 1postal stamps =

Similarly, the area occupied by 120such postal stamps

= 4×120 = 480cm²

∵ 45 persons can complete a work in 20days.

∴ 1 persons can complete a work in 45× 20i.e 900days

Similarly, 75 persons can complete the same work in

= 12× 24 = 288 h

∵Devangi covers the distance in75 steps = 50m

So, she covers the distance in 1 step =

In 375 steps, she will cover

⇒

⇒

⇒

⇒ 0.25km

False

Two quantities x and y are said to vary directly with each other, if x_y = k(constant)

False

When the speed is kept fixed, time and distance vary directly each other.

False

When the distance is kept fixed and time vary directly / inversely with each other. Since, if we increase speed, then taken time will less and vice-a-versa.

False

Length of a side of a square and its area does not vary directly with each other, e.g. Let a be length of each side of a square.

So, area of the square = side² = a²

So, if we increase the length of the side of a square, then their area increases but not directly.

False

Length of a side of an equilateral triangle and its perimeter vary directly with each other, e.g. let a be the side of an equilateral triangle. So, perimeter = 3 × (side) = 3× a = 3a. so, if we increase the length of side of the equilateral triangle, then their perimeter will also increase.

False

If d varies inversely as t^2, then we can write dt² = k, where k is some constant.

Since, two quantities x and y are said to be in inverse proportion, if an increase in x cause a proportional decrease in y and vice-a-versa, in such a manner that the product of their corresponding values remains constant.

True

∵Height of a tree = 24m

Then its shadow = 15m

With the similar condition, if a pole has a shadow of length = 6m

Let the height of pole = x m

Since, length and shadow vary directly.

Then,

⇒ 15× x = 24× 6

⇒

⇒ x = 9.6m

False

If x and y are in direct proportion, then

⇒

E.g. Let x = 4 and y = 6

∴

Now, x-1 = 4-1 = 3 and y-1 = 6-1 = 5

∴

False

If x and y are in inverse proportion, then xy = k(constant) e.g. Let x = 2 and y = 3

∴ xy = 2 × 3 = 6. Now, x + 1 = 2 + 1 = 3 and y + 1 = 3 + 1 = 4

Then, (x + 1) (y + 1) = 3×4 = 12 [not in inverse proportion]

Hence, (x + 1) and (y + 1) cannot be in inverse proportion.

False

If p and q are in inverse proportion, then

xy = k(constant)

e.g. Let p = 3 and q = 4

Then, pq = 3×4 = 12

Now, p + 2 = 3 + 2 = 5 and q-2 = 4-2 = 2

(p + 2) (q-2) = 5×2 = 10 [not in inverse proportion]

Hence, (p + 2) and (q-2) cannot be in inverse proportion.

False

If one angle of a triangle is kept fixed, then the measure of the remaining two angles can’t vary inversely with each other.

e.g. In ΔABC, ∠A + ∠B + ∠C = 180° [sum of all angles of a Δ]

if ∠A = 50°, then ∠B + ∠C = 180° -50° = 130°

So, it is not depending on any proportion by applying angle sum properties of a triangle.

True

When two quantities are related in such a manner that if, one increases the other also increases, then they always vary directly.

Above statement is correct for direct proportion. It is a basic property of direct proportion.

True

When, two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely. Above statement is correct for inverse proportion. It is a basic property of inverse proportion.

False

If x varies inversely as y, i.e. xy = k(constant)

If x = 6 and y = 8

∴ xy = 6×8 = 48

But if x = 8 and y = 10

∴ xy = 8 × 10 = 80

Here, 48 ≠80

Hence, the value of y is not 10

False

The number of workers and the time to complete a job is a case of indirect proportion, e.g. if 160 workers can complete a work in 10 days.

Then, 120 workers can complete the same work in 5 days.

True

For fixed time period (T) and rate of interest(R), the simple interest is directly proportional to the principal.

We know that,

⇒ = Constant (as R and T asre constants)

∴ simple interest is directly proportional to the principal.

True

The area cultivated land and the crop harvested in a case of direct proportion.

Since, the quantities of crop harvested is depend upon area of cultivated land.

1: The time taken by a train to cover a fixed distance and the speed of the train are inversely proportional.

E.g. If train cover 100km in 1h with speed 100km/h.

Then, the same train cover 100km in 1h with speed 200km/h.

2: The distance travelled by CNG bus and the amount of CNG used are directly proportional. E.g. if CNG bus can travel 10km in 1 kg of CNG.

Then, the same CNG bus can travel 20km in 2kg CNG.

3: The number of people working and the time to complete a

given work are inversely proportional to each other.

e.g. If 20 workers can complete a work in 1day.

Then, 10 workers can complete the same work in 2days.

4: Income tax and the income are directly proportional to each

other, e.g. If Mr.X have 4.5 lakh annual income.

Then, he pays 10% income tax on his income

But if Mr.X have 5.5 lakh annual income, then he has to pay 30% income tax on his income.

5: Distance travelled by an auto rickshaw and time taken are directly proportional to each other.

e.g. If an auto rickshaw takes 2h travel 10km

Then, it will take 4h to travel 20km.

(i): Number of students in a hostel and consumption of food are direct proportional to each other.

e.g. if 200 students in a hostel can consume 100kg of rice in a month. Then, 400 students in hostel can consume 200kg of rice in a month.

(ii): Area of the walls of a room and the cost of white washing

the walls are directly proportional to each other.

e.g. if ₹ 1000 required for white washing a room with

(12× 8) m size. Then, ₹ 2000 is required to white wash a

room with (12× 16) m size.

(iii): The number of people working and the quantity of work

are directly proportional to each other.

e.g. If 20 workers can complete 20 of a work. Then, 40 workers can complete 40 of the same work.

(iv): Simple interest on a given sum and the rate of interest

are directly proportional to each other.

e.g. Let p = R = 10% and T = 1yr.

∴

But if P = ₹ 1000, R = 20 and T = 1yr.

∴

(v): Compound interest on a given sum and the sum invested are neither depend directly nor inversely.

i. The quantity of rice and its cost are directly proportional to each other.

e.g., If 1 kg of rice price = ₹ 40. Then, 2kg of rice price = ₹ 2 × 40 = ₹ 80.

ii. The height of a tree and the number of years is neither directly nor inversely proportional to each other.

iii. Increase in cost and number of shirts that can be purchased if the budget remains the same is inversely proportional to each other.

e.g. If 2 shirt’s prices = ₹ 800. After increase in price each price.

1 shirt price becomes of ₹ 800 where budget = ₹ 800.

iv. Area of land and its cost are directly proportional to each other.

e.g. Let 200m² land cost = ₹ 5000

Then, 400m² land cost = ₹ 10,000

v. Sales tax and the amount of the bill are directly proportional to each other.

e.g. Let bill amount = ₹ 1000

Sales tax = 10

Then, sales tax =

But if, bill amount = 2000

Sales tax = 10

Then, sales tax =

If x varies inversely as y.

∴ xy = k(constant) …(i)

If x = 20 and y = 600

∴xy = 20× 600 = 12000

⇒ k = 12000

When x = 400, then from Eq. (i)

y× 400 = k

⇒ y × 400 = 12000

⇒

If x varies directly as y.

∴

If x = 80 and y = 160 …(i)

∴

⇒

When x = 64, then from Eq. (i)

⇒ y = 64 × 2 = 128

If l varies directly as m.

∴

If

∴

⇒

⇒ k =

When

⇒

If x varies inversely as y

∴ xy = k (constant)

If x = 1.5 and y = 60

∴

⇒ k = 90

When y = 4.5, then from Eq.(i),

45× y = k

⇒ 45 × y = 90

⇒ 20

∵For 300 persons flour is enough for 42 days.

∴ For 1 person’s flour enough = 300 × 42 = 1260days.

Now, 20more persons join the camp.

SO, total persons = 300 + 20 = 320

∴ for 320 persons flour enough = days

∵ In 9 months, a part of stadium can complete by 560persons.

∴ In 1 month, the work can be complete by 9× 560 = 5040 persons.

∵ In 5 months, the work can be complete by

Sobi can types 108 words in 6 min.

In 1 min, she can type =

Thus, in 30min, she can type =

A car covers a distance in 40 min with an average speed =

60km/h = m/min

In 1 min, the same distance can be cover with speed =

m/min

In 25 min, the same distance can be cover with speed =

m/min

Since l varies directly as m.

a. Equation related to l and m is

b. If

c. If m = 33, then

⇒

⇒ ⇒

d. if

∴ ⇒

⇒ m = 8× 3 = 24

If deposit of ₹ 2000 earns in 3yr with an interest = ₹ 500

Then, a deposit of ₹ 1000 earns in 3yr with an interest =

Similarly, deposit of ₹ 3600 i.e. ₹ 36 × 1000 earns in 3yr with an interest = 250×36 = ₹ 9000

According to the question, the mass(m) of an aluminium rod varies directly with its length(l). Here, we use the direct proportion.

In direct proportion,

∴

⇒ k = 12

If mass of the rod = 105g

Then,

⇒

⇒ cm

In an inverse proportion,

When we multiply the first quantity by any constant k, then another quantity is divided by the same constant k.

Given,

Here, we see that in part (b) when we divide 30by 6, we will get 5.

So, in part(a), we will get the value of x.

i.e. x = 12×6 = 72

Similarly, in part(a) when we divide x i.e.72 by 9, we will get 8.

So, in part(b) we will get the value of y.

i.e. y = 5×9 = 45

∵ Naresh walks 250 steps to cover distance = 2000m

∴ in 1 step, he covers the distance = m

∵ In 350, steps, he covers = =

= m

A car travels 225km distance in 25L petrol.

∵ for 1 km, petrol required =

∴ For 540 km, the petrol required =

In direct proportion, = k(constant)

For table (a),

⇒

i.e.

So, (a) is not in direct proportion.

For table b,

⇒

i.e.

So, (b) is in direct proportion.

For table (c)

⇒

i.e.

so, (c) is in direct proportion.

If a and b vary inversely to each other.

i.e. ab = k(constant)

For table (a),

If a = 6 and b = 18

Then, a

⇒ k = 108

When a = 8 and b = p, then

ab = k

⇒ 8×p = 108

⇒

When a = q and b = 39, then

ab = k

∴ q× 39 = 108

⇒

When a = 25 and b = r, then

ab = k

⇒ 25 × r = 108

⇒

For table (b),

If a = 6 and b = 15

Then, a

⇒ k = 90

When a = 2 and b = x, then

ab = k

⇒ 2× x = 90

⇒

When a = y and b = 12.5, then

ab = k

∴ y× 12.5 = 90

⇒

When a = 10 and b = z then

ab = k

⇒ 10 × z = 90

⇒

For table (c),

If a = 6 and b = 1

Then, a

⇒ k = 60

When a = l and b = 5, then

ab = k

⇒ l×5 = 60

⇒

When a = 9 and b = m, then

ab = k

∴ 9× m = 60

⇒

When a = n and b = 25, then

ab = k

⇒ n × 25 = 60

⇒

According to the question,

∵ 25m of cloth cost = ₹ 337.50

∴ 1m of cloth cost = ₹

a) Cost of 40 m of the same type of cloth =

b) The length of cloth bought for ₹ 810 =

A swimming pool can be filled in 4 hours by 8pumps.

If we want to fill the swimming pool in 1h,

we required 4×8 = 32pumps

in the number of pumps required = 32

∵ The cost of 27kg of iron = ₹ 1080

∴ Cost of 1kg of iron =

∴ The cost of 120 kg = 40×20 = ₹ 4800

Hence, the cost of 120kg of iron is ₹ 4800

∵Length of Qutub Minar = 72m

Its shadow at particular time = 80m

Length of shadow of electric pole = 1000cm = 10m

∴ Length of electric pole =

In a hostel of 50 girls, food is available = 40days

For 1 girl, food provision = 50× 40 = 2000days

Now, for (50 + 30) girls i.e. 80girls, the food provision =

⇒ 25 days

The food provision will last for 25 days, if 30 more girls join.

i. In mixture A,

The number of blue containers = 3

The number of white containers = 4

∴ Ratio of blue and white =

In mixture B,

The number of blue containers = 3

The number of white containers = 3

∴ Ratio of blue and white =

Clearly, mixture A would be lighter shade.

ii. In mixture C,

The number of blue containers = 3

The number of white containers = 3

∴ Ratio of blue and white =

In mixture D,

The number of blue containers = 2

The number of white containers = 5

∴ Ratio of blue and white =

Clearly, mixture A would be lighter shade.

iii. In mixture E,

The number of blue containers = 6

The number of white containers = 1

∴ Ratio of blue and white =

In mixture F,

The number of blue containers = 4

The number of white containers = 2

∴ Ratio of blue and white =

Clearly, mixture F would be lighter shade, since for lighter shade white container should be equal or more than or nearest number of blue container.

iv. In mixture G,

The number of blue containers = 3

The number of white containers = 3

∴ Ratio of blue and white =

In mixture H,

The number of blue containers = 4

The number of white container = 3

∴ Ratio of blue and white =

Clearly, mixture G would be lighter shade, since for lighter shade white container should be more than blue container.

From the above all mixtures, mixture D is lightest among them.

∴ The total number of containers required for painting = 105

∴ Number of blue container required for painting =

∴ Number of white containers required for painting =

On the basis of given figure in which white, blue and purple squares are given.

∴ Purple = 12, Blue = 20 and white = 16

Total squares = 12 + 20 + 16 = 48

Statement I Purple: Total = 12:48 = 1:4

Statement II Blue: Total = 20:48 = 5:12

Statement III White: Total = 16:48 = 1:3

Statement IV Purple: Blue = 12:20 = 3:5

Statement V Purple: White = 12:16 = 3:4

The total number of children = 10

If each child received 4 Sweets, then the total number of sweets = 10× 4 = 40sweets.

If 40 sweets distributed between 8 children, then each get i.e. 5 sweets.

44 cows can graze a field = 9 day

The number of cows that can graze the same field in 1 day

= 44× 9 cows

In 12 days, the number of cows required = cows

∵30 persons can reap a field in 17 days.

1person can reap the same field in 30×17 i.e. 510dats.

In 10 days, the number of persons required = persons.

Shabnam’s speed = 6 km/h = m/min

∴ Total distance covered by Shabnam in 20min =

=

= 2000m

If she wants to reach the school in 24 min, then should maintain the speed =

= m/min

= km/h

Let the total distance = x km

Let the time taken by Ravi to reach the school at sharp time = t min

If the speed of the bicycle is 10km/h, then he reaches his school late by 8 min

∴

⇒ (1)

If the speed of the bicycle is 16km/h, then he reaches his school 10min early.

∴

⇒ (2)

On subtracting equation (2) from (1)

⇒

⇒

⇒

⇒

Now, put x = 8 in Eq. (i),
we get

⇒

Hence starting time of school is 8:20 + 40min i.e. 9:00am

In 20g of sauted fish, protein is 75g

∴ In 1g of souted fish, Protein is

In 225g of sauted fish, protein =

The distance between Jhareda to Ganwari in the map = 3.5cm

Given scale, 1cm = 10km

So, actual distance between the villages = 35×10 = 35km

The height of the tree = 9.5m

The shadow of the tree = 8m

According to the given condition in the question, the lengths of the shadow are in direct proportion.

∴

⇒

on the basis of given table

Elevator A takes 29s to cover 435m

∴Distance covered by elevator A in 1s =

Elevator B takes 28s to cover 448m.

∴Distance covered by elevator B in 1 s =

Elevator C takes 10s to cover 130m

∴Distance covered by elevator C in 1s =

Elevator D takes 5s to cover 85 m

∴Distance covered by elevator D in 1s =

Hence, in 1s, elevator D covers more distance as compare to elevator A, B and C. so, elevator D is fastest, while elevator C covers least.

Hence elevator C is slowest.

Now, elevator B covers distance in 140s = 140× 16 = 2240m

Elevator C covers distance in 140s = 140× 13 = 1820m

∴Elevator B covers more distance than C = 2240-1820 = 420m

From the given figures,

Length of volleyball court = 18m

Breadth of volleyball court = 9m

Length of pool = 75m

Let the width of swimming pool = x m

According to the question, the size of volleyball court and swimming pool are in direct proportion to each other.

∴

⇒

Hence, the width of the swimming pool is 37.5m

A particular type of muffins requires 1cup of milk and 1.5 cups of chocolates.

Riya has 7.5 cups of chocolates.

The number of cups of milk required for 7.5cups of chocolates =

The number of red dots in pattern A (•) = 4

The number of blue dots in pattern A (⃘) = 2

Pattern B consists of four tiles like pattern A i.e.

Patter A × 4 = Pattern B

∴ Proportion in pattern =

Now, proportion of blue dots and red dots in pattern B =

The speed of the cricket ball = 120km/h

⇒ m/min

⇒ 2× 1000

⇒2000 m/min

Now, speed in m/s =

So, 20m can be cover in

The variable x is inversely proportional to y.

xy = k(constant)

since, we know that two quantities x and y are said to be in inverse proportion, if an increase in x cause a proportional decrease in y and vice-a-versa. So, we can say y decreases by p

According to the given figure,

(a) The total number of black keys = 7

The total number of white keys = 10

Hence, the ratio of white keys to black keys on the keyboard =

(b) The total number of all keys = 10 + 7 = 17

The ratio of black keys to all keys on the given keyboard =

(c) Black keys in 1 keyboard = 7

Black keys in 14 such keyboards = 14× 7 = 98 keys.

On the basis of given table, the distance travelled by one new eco-friendly energy-efficient earns travelled on gas.

The car travelled 15 km in 1L of gas

The car travelled 7.5 km in 0.5L of gas

The car travelled 30 km in 2L of gas

This rate shows direct proportion between litres of gas and the distance cover.

The car can cover the distance in 8L of gas = 8× 15 = 120km

After used of most of sugar syrup for her breakfast, the remaining sugar is cup of sugar syrup. Thus, it means has been used. She needs cup of sugar syrup for one piece of bread. So, new quantity of ingredient will be in proportion of

Now the bread recipe will be look like

cup quick cooking oats 1 cup bread flour

cup sugar syrup tablespoon cooking oil

tablespoon yeast cup water

tablespoon salt

Students: teacher ratio = 35:1

It shows every 35 students-one teachers should available in the school.

In the school, number of teachers required for 280 students = = teachers.

50 miles per hour is same as travelling 80km per hour.

So, 1 km covers distance in 1h to miles.

To cover a distance of 200 km =

Hence, 125 miles Kusum has to go for 200km.

a) Every 60 posters, Anju’s class students raise = ₹ 250

So, from 1 poster, Anju’s class students raise =

If Anju sell 102 posters, then they raise =

Hence, Anju’s class make ₹ 425 by selling of 102 posters.

b) Since, by selling 1 poster, Anju’s class raise = ₹

For raising exactly ₹ 2000, they need to sell =

= posters.