Question

A merchant has 3 varieties of sugar with their quantity in the ratio of 1 : 3 : 5. If a certain amount of the first variety and 17 kg of the second variety are added to their initial quantity and 12 kg of the third variety is removed from it, the final ratio of the three varieties becomes 2 : 4 : 3. Find the amount of first type sugar added.
1. 10 kg
2. 11 kg
3. 12 kg
4. 13 kg

Answer 1

Correct Answer - Option 4 : 13 kg

GIVEN:

Initial quantity ratio = 1 : 3 : 5

Quantity of 2nd variety added = 17 kg

Quantity of 3rd variety removed = 12 kg

Final ratio = 2 : 4 : 3

EXPLANATION:

Let initial quantities be 1x, 3x, 5x and added quantity of first type be 'a'

A.T.Q 

x + a : 3x + 17 : 5x - 12 = 2 : 4 : 3

(3x + 17)/(5x - 12) = 4/3

9x + 51 = 20x - 48

11x = 99 ⇒ x = 9 

(x + a)/(5x - 12) = 2/3

(9 + a)/(33) = 2/3

27 + 3a = 66

a = 13 kg

∴ 13 kg of 1st type was added