Question

An adulterant mix white colour in milk and make two solutions of colour and milk in the ratio 9 ∶ 7 and 5 ∶ 8. Find the proportion in which the two solutions should be mixed so that the resulting solution has 2 part colour and 3 parts milk?
1. 13 ∶ 21
2. 21 ∶ 17
3. 1 ∶ 13
4. None of these

Answer 1

Correct Answer - Option 3 : 1 ∶ 13

Given∶

Two altered solutions of white colour and milk are in the ratio of 9 ∶ 7 and 5 ∶ 6.

Resulting solution has 2 parts of colour and 3 parts of milk.

Formula Used∶

a ∶ b ∶∶ c ∶ d

Then, a/b = c/d

Calculation∶

Given∶

Let the quantity of colour and milk in first solution be 9x and 7x while their quantity in second solution be 5y and 8y respectively.

So,

(9x + 5y)/(7x + 8y) = 2/3

⇒ 27x + 15y = 14x + 16y

⇒ 13x = y

⇒ x/y = 1/13

∴ 1/13 is the proportion in which these two solutions should be mixed.