A sum of ₹7,560 is divided between A, B and C such that the ratio of the share of A to the combined share of B and C is 5 : 9 and the ratio of the share of C to the combined share of A and B is 3 : 7. What is the share of B?

Correct option is B

Given:

Total sum = ₹7, 560

A : (B + C) = 5 : 9

C : (A + B) = 3 : 7

Find: Share of B

Solution:

Ratio of A to (B+C):

The ratio of A's share to the combined share of B and C is given as 5 : 9.

This means A's share is $$\frac 5{5+9}​=\frac 5{14}$$​​ of the total sum.

Ratio of C to (A+B):

The ratio of C's share to the combined share of A and B is given as 3 : 7.

This means C's share is $$\frac{3}{3+7}​=\frac 3{10}$$​ of the total sum.

Calculate A's and C's shares:

A's share =$$\frac 5{14}​ ×7560 =2700$$​​

C's share ​=$$\frac 3{10} ×7560=2268$$​​

Calculate B's share:

The total sum is ₹7,560.

B's share = Total sum - (A's share + C's share)

B's share = 7560 − (2700 + 2268)

B's share = 7560 − 4968

B's share = ₹2592