Question

Three boys A, B and C got different number of pens. If A gives 3 pens to C, then the ratio of the number of pens of A and C becomes 19 ∶ 28. If B gives 2 pens to C, then the ratio of the number of pens of B and C will be 7 ∶ 11. The number of pens with B is 37. Find the number of pens with A.
1. 53
2. 33
3. 41
4. 55

Answer 1

Correct Answer - Option 3 : 41

Given:

If A gives 3 pens to C, ratio becomes = 19 ∶ 28.

If B gives 2 pens to c, ratio becomes = 7 ∶ 11

The number of pens with B = 37

Calculation:

Let the pens with A, B and C be a, b and c respectively.

If B gives 2 pens to c, ratio becomes = 7 ∶ 11

⇒ (b – 2)/(c + 2) = 7/11

⇒ (37 – 2)/(c + 2) = 7/11

⇒ 385 = 7(c + 2)

⇒ c = 53

Now, If A gives 3 pens to C, ratio becomes = 19 ∶ 28

⇒ (a – 3)/(c + 3) = 19/28

⇒ (a – 3)/(53 + 3) = 19/28

⇒ a = 38 + 3

⇒ a = 41

∴ The number of pens with A is 41.