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Mixture

Class 8th Mathematics West Bengal Board Solution
Lets Work Out 12
  1. The ratio of measurements of water and Dettol in 36 litres of water is 5:1. Let’s work…
  2. In a certain type of brass the ratio of measurements of Copper and Zinc is 5:2. Let’s…
  3. Bijan babu has made phenyl water solution of 60 litres in which the ratio of…
  4. Amina Bibi has prepared masonry mixture with sand and cement in a ratio of measurement…
  5. The ratio measurements of Copper, Zinc and Nickel in German silver is 4:3:2…
  6. In two different kinds of washing powder the ratios of measurement of soda and soap…
  7. 1 and parts two similar vessels contain fruit juice. I filled water in the remaining…
  8. Reshmi Khatun has filled 3 similar glasses of equal size with beverage. The ratios of…
  9. Two different types of brass coating Copper and Zinc in the ratio of measurement 8:3…
  10. Two different types of stainless steel contain Chromium and Steel in the ratio of…
  11. In a vessel of beverage the ratio of measurement of syrup and water is 5:2. Let’s work…
  12. Let’s see the table below, write in mathematical language and try to find out the…
  13. There are three kinds of liquid in a beverage of 700 liters. The ratio of measurements…
  14. The ratio of water and the remaining portion in a syrup in 89:11. How much liters of…
  15. The ratio of the volumes of three bottles is 5:3:2. These three bottles are filled…
Lets Work Out 12
Question 1.

The ratio of measurements of water and Dettol in 36 litres of water is 5:1. Let’s work out what volume of dettol should be added to the mixture so that the ratio of measurements of water and dettol becomes 3:1.
Answer:

Given that water and Dettol ratio is 5:1 and the mixture is 36 liters.


So, volume of Dettol


We have, Volume of water


According to given questions:


Let “x” liters of Dettol be added.


Ratio of measurement of water and Dettol is 3:1


So,



⇒ 30 = 3(6+x)


⇒ 18 + 3x = 30


⇒ 3x = 30-18


⇒ 3x = 12


⇒ x = 4


So, 4 liters Dettol should be added to mixture.
Question 2.

In a certain type of brass the ratio of measurements of Copper and Zinc is 5:2. Let’s work out what will be the ratio of Copper and Zinc in 28 kg of brass if 4 kg of Copper is added to it.
Answer:

Given,


The ratio of copper and zinc in mixture = 5:2


Let copper in mixture is “5a”.


So, zinc will be “2a”.


Given that quantity of brass (mixture of copper and zinc) = 28 kg


⇒ quantity of copper+ quantity of zinc = 28


⇒ 5a + 2a = 28


⇒ 7a = 28


Or, a = 4


So, quantity of zinc = 2a = 2×4 = 8 kg


Also, quantity of copper = 5a= 5×4= 20 kg


According to given problem,


If we add 4 kg of copper


Then quantity of copper in mixture = 20+4 = 24kg


So, the ratio of copper and zinc in 28 kg of brass


= 3:1
Question 3.

Bijan babu has made phenyl water solution of 60 litres in which the ratio of measurements of phenyl and water is 2:23. Let’s work out how much phenyl should be added to this solution so that the ratio of measurements of phenyl and water becomes 9:46.
Answer:

Quantity of phenyl litres = 4.8 liters


Quantity of water in mixture = (60 ─ 4.8) liters = 55.2 litres


New ratio = 9: 46


Let quantity of phenyl to be added further be “x” liters.


Then,



⇒


⇒ 220.8 + 46x = 496.8


⇒ 46x = 496.8 ─ 220.8


⇒ 46x = 276


⇒ x = 6


Quantity of phenyl to be added = 6 litres.
Question 4.

Amina Bibi has prepared masonry mixture with sand and cement in a ratio of measurement 7:1. But after the brick-work it is seen that 72 kg of mixture remains. She has added more cement with this mixture and the ratio of measurement of sand to cement becomes 6:1. Let’s work out the total quantity of cement she has mixed.
Answer:

The ratio of mixture of sand and cement is 7:1,


This means total part of mixture is 8


Out of which 7 parts is sand and 1 part is cement,


Quantity of sand


= 7 × 9


= 63 kg


Quantity of cement


= 9 kg


72 kg of mixture is equal to 63 kg of sand and 9 kg of cement.


Let “x” kg cement is added,


Now ratio of sand to cement becomes 6:1.



⇒ 63 = 6(9 + x)


⇒ 63 = 54 + 6x


⇒ 63-54 = 6x


⇒ 9 = 6x


⇒ x = 1.5 kg
Question 5.

The ratio measurements of Copper, Zinc and Nickel in German silver is 4:3:2 respectively. Let’s work out what weight (in kgs) of Zinc should be added to 54 kg of German Silver, so that the ratio of measurements become 6:5:3.
Answer:

The ratio of mixture of copper, zinc and nickel is 4:3:2


Quantity of zinc in the initial


= 18 kg


Let a kg of zinc added to make ratio 6:5:3


According to new ratio 6:5:3


Ratio of nickel to German silver =


⇒


⇒ 252 + 14a = 270 + 5a


⇒ 14a – 5a = 270 – 252


⇒ 9a = 18


⇒ a = 2 kg


So, 2kg of zinc to be added in mixture.
Question 6.

In two different kinds of washing powder the ratios of measurement of soda and soap powder are 2:3 and 4:5. Let’s work out the part of the soap powder in the new washing powder which is prepared by mixing 10 kg of first washing powder with 18kg of second washing powder.
Answer:

The ratio of mixture of soda and soap in first kind of washing powder = 2:3


The ratio of mixture of soda and soap in second kind of washing powder = 4:5


Concentration of soap as fractions in first kind washing powder



Concentration of soap as fractions in second kind washing powder →



mixing 10 kg of first washing powder with 18kg of second washing powder, then →


Quantity of new washing powder = (10 + 18) kg = 28 kg


Quantity of soap in new washing powder


= 6 + 10 = 16 kg


Quantity of soda in new washing powder = 28 – 16 = 12 kg


Hence, ratio of soda to soap = 12:16


= 3: 4


Part of soap water in the new washing powder is 4/7.
Question 7.

and parts two similar vessels contain fruit juice. I filled water in the remaining empty part of these vessels and poured the juice mixed with water of the two vessels into another big vessel. Let’s work out the ratio of measurement of fruit and water in the new vessel.
Answer:

Let the capacity of vessel be 12 units.


Fruit juice in first vessel


= 4 units


Water in first vessel = 12 – 4 = 8 units


Fruit juice in second vessel


= 3 units


Water in second vessel = 12 – 3 = 9 units


Total fruit juice = 4 + 3 = 7 units


Total water = 8 +9 = 17 units


Fruit juice: Water = 7: 17
Question 8.

Reshmi Khatun has filled 3 similar glasses of equal size with beverage. The ratios of measurements of water and syrup in these three glasses are 3:1, 5:3 and 9:7 respectively. I poured the beverage of these three glasses into a big vessel. Let’s work out the ratio of measurements of water and syrup in the new vessel.
Answer:

ratio of water and syrup in first glass = 3:1


ratio of water and syrup in second glass = 5:3


ratio of water and syrup in third glass =9:7


Let the capacity of glass be 12 units.


So,


Quantity of water in first glass units


= 9 units


Quantity of syrup in first glass = 12 – 9 = 3 units


Quantity of water in second glass 7.5 units


Quantity of syrup in second glass = 12 – 7.5 = 4.5 units


Quantity of water in third glass 6.75 units


Quantity of syrup in third glass = 12 – 6.75 = 5.25 units


Total quantity of water = 9 + 7.5 + 6.75 = 23.25 units


Total quantity of syrup = 3 + 4.5 + 5.25 = 12.75 units


So, ratio of water and syrup in new vessel


Water: syrup = 31: 17
Question 9.

Two different types of brass coating Copper and Zinc in the ratio of measurement 8:3 and 15:7 respectively. Let’s work out what the ratio of measurement of Copper and Zinc will be if these two types of brass are mixed together in the ratio of measurement 5:2.
Answer:

Ratio of copper and zinc in first type of brass = 8:3


Ratio of copper and zinc in second type of brass = 15:7


So,


Ratio of copper in first type of brass


These two types of brass are mixed together in the ratio of measurement 5:2


First type brass copper in new ratio 5:2


Ratio of copper in second type of brass


Second type brass copper in new ratio


ratio of zinc in first type of brass


first brass zinc in new ratio 5:2


second type zinc in new ratio


so, ratio of copper to zinc in new ratio 5:2








ratio of copper to zinc in new ratio 5:2 = 5:2
Question 10.

Two different types of stainless steel contain Chromium and Steel in the ratio of measurement of 2:11 and 5:21 respectively. Let’s work out in what proportion these two types of steel should be mixed, so that the ratio of measurement of Chromium and Steel becomes 7:32.
Answer:

Ratio of chromium and steel in first type stainless steel = 2:11


Ratio of chromium in first type stainless steel


Ratio of steel in first type stainless steel


Ratio of chromium and steel in second type stainless steel = 5:21


Ratio of chromium in second type stainless steel


Ratio of steel in second type stainless steel


Suppose kg of first type and y kg of second type stainless steel taken and mixed so that the ratio of measurement of Chromium and Steel becomes 7:32


Then, ratio of chromium in new mixture


Quantity of chromium in new mixture


Total quantity of new mixture = (x +y)


hence,




⇒


⇒ 12x + 15 y = 14x + 14y


⇒ 14x – 12x = 15y – 14y


⇒ 2x = y


⇒


x: y = 1:2
Question 11.

In a vessel of beverage the ratio of measurement of syrup and water is 5:2. Let’s work out what part of the drink should remove and replaced by water so that the volume of syrup and water becomes equal.
Answer:

Let the mixture of syrup and water is “x” litres.


So,


Volume of syrup in the mixture


Volume of water in the mixture


Let “y” = Volume of mix taken out = Volume of water added


When a part of drink is taken out:


In the drink the ratio will remain same:


So,


Volume of syrup is


Volume of water is


After a part is taken out:


Volume of syrup in vessel


Volume of water in vessel


After water is added,


Volume of water


According to the question:


Volume of water added = volume of syrup




⇒ 2x – 2y + 7y = 5x – 5y


⇒ 2x + 5y = 5x – 5y


⇒ 2x + 5y = 5x – 5y


⇒ 5y + 5y = 5x – 2x


⇒ 10y = 3x



Hence the volume of water added is 3/10 part of the vessel.
Question 12.

Let’s see the table below, write in mathematical language and try to find out the answer.
Answer:

For easy way let assume given mixture is of milk and water


1. ratio of milk and water in first type of mixture = 5:4


ratio of milk and water in second type of mixture = 3:2


milk in first type of mixture


Water in first type mixture


Milk in second type of mixture


Water in second type of mixture


Given that equal quantities are taken from two mixture. Let x unit is taken from both mixtures.


So, milk in new type of mixture =






And, water in new mixture =





Hence,


Ratio of milk to water in new mixture




Milk: water = 26:19


2. For easy way let assume given mixture is of milk and water


ratio of milk and water in first type of mixture = 4:5


ratio of milk and water in second type of mixture = 5:1


ratio of milk and water in new mixture = 5:4


Suppose kg of first type and y kg of second type taken and mixed


Quantity of milk in in new mixture



Total quantity of new mixture = ( )


Hence,



8 + 15y = 10 + 10y


⇒ 2 = 5y


⇒ x: y = 5:2


3. ratio of milk and water in first type of mixture = 3:4


ratio of milk and water in second type of mixture = 9:5


For easy way let assume given mixture is of milk and water


milk in first type of mixture


Water in first type mixture


Milk in second type of mixture


Water in second type of mixture


Given that, the ratio of the quantities of two mixtures in the new mixture is 1:2


So, milk in new type of mixture


And, water in new mixture


Hence,


Ratio of milk to water in new mixture


Milk: water = 4:3


4. For easy way let assume given mixture is of milk and water


ratio of milk and water in first type of mixture = 2:3


ratio of milk and water in second type of mixture = 5:4


ratio of milk and water in new mixture = 1:1


Suppose x kg of first type and y kg of second type taken and mixed


Quantity of milk in in new mixture





Total quantity of new mixture = ( )


Hence,





⇒ 9= 5y


⇒ : y = 5:9


5. For easy way let assume given mixture is of milk and water


ratio of milk and water in first type of mixture = 4:3


ratio of milk and water in second type of mixture = 5:2


ratio of milk and water in new mixture = 9:5


Suppose kg of first type and y kg of second type taken and mixed


Quantity of milk in in new mixture





Total quantity of new mixture = ( )


Hence,




⇒ 8+ 10y = 9 + 9y


⇒ = y


⇒ : y = 1: 1
Question 13.

There are three kinds of liquid in a beverage of 700 liters. The ratio of measurements of the first and the second liquids is 2:3 and the ratio of measurement of the second and the third liquid is 4:5. Let’s work out the ratio in which the first and second liquid will be mixed so that the ratio of measurement of the three liquids become 6:5:3 in the new beverage.
Answer:

Given,


Ratio of first, second and third liquid.


First liquid : second liquid : third liquid


2 : 3


4 : 5


Quantity of second quantity will be same, so to make it equal, multiply by 4 in upper no.’s and by 3 in lower no’s


First liquid : second liquid : third liquid


2×4 : 3×4


4×3 : 5×3


8 : 12 : 15


So, Ratio of first, second and third liquid in beverages = 8:12:15


Beverage is of 700 liters


New ratio of liquids in mixture = 6:5:3


So, quantity of first type of liquid in new mixture





quantity of second type of liquid in new mixture





Ratio of first and second type liquid




=6:5
Question 14.

The ratio of water and the remaining portion in a syrup in 89:11. How much liters of water are to be added to the syrup to make the ratio 90:10?
Answer:

Ratio of water to remaining part of syrup is 89:11


Total parts = 89+11= 100 parts


Let syrup be liters


litres of water and litres of remaining syrup.


When ‘y’ litres of water is added ratio becomes 90:10 i.e. 9:1


Therefore,






⇒ 89 – 100y = 99


⇒ 10 = 10y




So, amount of water to be added is parts of the total syrup.
Question 15.

The ratio of the volumes of three bottles is 5:3:2. These three bottles are filled with the solution of phenyl and water. The ratios of measurement of phenyl and water in three bottles each are 2:3, 1:2 and 1:3 respectively. part of the first bottle, part of the second bottle and part of the third bottle are mixed together now. Let’s work out ratio of phenyl and water in the new solution.
Answer:

Let the volumes of three bottles are 60, 36, 24 litres.


Then phenyl in first bottle litres


& water in first bottle liters


Phenyl in second bottle litres


Water in second bottle litres


Phenyl in third bottle litres


Water in third bottle litres


Quantity of phenyl in new mixture



Quantity of water in new mixture



So, the ratio of phenyl & water in new mixture = 18: 36


= 1: 2