Correct Answer - Option 4 : 13 ∶ 22
Given:
If A would have obtained 7 more marks, then the ratio of marks of A and B would have been 3 ∶ 4.
Had B scored 5 less marks, then the ratio of marks of A and B would have been 2 ∶ 3.
Formula:
If the ratio of A and B is a ∶ b, assume A = ak and B = bk
Where k is a constant.
Calculation:
let marks scored by A and B be a and b respectively.
If A would have obtained 7 more marks, then the ratio of marks of A and B would have been 3 ∶ 4.
So, (a + 7)/b = 3/4
⇒ 4a + 28 = 3b
⇒ 3b – 4a = 28 ----(1)
Had B scored 5 less marks, then the ratio of marks of A and B would have been 2 ∶ 3.
So, a/(b – 5) = 2/3
⇒ 3a = 2b – 10
⇒ 2b – 3a = 10 ----(2)
Multiply equation (1) by 2 and equation (2) by 3
2 × (3b – 4a) = 2 × 28
⇒ 6b – 8a = 56 ----(3)
3 × (2b – 3a) = 3 × 10
⇒ 6b – 9a = 30 ----(4)
Subtracting equation (3) from equation (4)
⇒ a = 26
Put the value of a in equation (2)
⇒ 2b – 3a = 10
⇒ 2b – 3(26) = 10
⇒ b = 44
The ratio of marks of A and B = 26 ∶ 44 = 13 ∶ 22
∴ The ratio of marts of A and B is 13 ∶ 22
