Question

27) A vessel contains 70 liters of a
mixture of milk and water containing 90
% milk. Find the quantity (in liters) of
water to be added to the vessel so that
the percentage of milk the new solution is
87.5%.
a)
b) 2
c)3
d) 4​

Answer 1

Answer:

2L of water must be added to the solution.

Option b. is correct.

Step-by-step explanation:

We have,

70L of a mixture of water and milk, and it contains 90% milk.

Now,

In a mixture, if there is 90% of milk then there will be,

(100 - 90)% of water.

= 10% of water

So,

The ratio of milk to water = 90 : 10

= 9 : 1

Thus,

If we take 10mL of this mixture, we will get 9 mL milk and 1 mL water

But, we have 70L of solution,

So,

Amount of milk = [ratio/(total ratio)] × Total amt. of sol.

Amt. of milk in 70L = [9/(9 + 1)] × 70

Amt. of milk in 70L = (9/10) × 70

Amt. of milk in 70L = 9 × 7

Amt. of milk in 70L = 63L

Similarly,

Amt. of water in 70L = (1/10) × 70

Amt. of water in 70L = 1 × 7

Amt. of water in 70L = 7L

Hence,

In our 70L mixture, there is 63L milk and 7L water, that is, 90% milk and 10% water.

Now,

We need 87.5% of milk, that means we need 12.5% of water.

So,

Let us add 'x' L of water into the solution.

Then,

Amt. of water = (7 + x)L

Total solution = (70 + x)L

Then, according to the Question,

12.5% = (7 + x)/(70 + x)

12.5/100 = (7 + x)/(70 + x)

Cross multiplying we get,

12.5(70 + x) = 100(7 + x)

875 + 12.5x = 700 + 100x

100x - 12.5x = 875 - 700

87.5x = 175

x = 175/87.5

x = 1750/875

x = 2L

Hence,

2L of water must be added to the solution.

Let's check it,

Amt. of milk = 63L

Total solution = 70 + 2 = 72L

Then,

Percentage of milk = (63/72) × 100

% of milk = 87.5%

Hence, it is correct.

Hope it helped and believing you understood it........All the best