A sum of ₹9240 is divided between A, B and C such that the ratio of C's share to the combined share of A and B is 3:8 and the ratio of B's share to the combined share of A and C is 2:5. What is the share of A?

Correct option is C

Given:

Total sum = ₹9240

​$$\frac{C}{A+B}= \frac{3}{8}, \quad \frac{B}{A+C}= \frac{2}{5}$$​​

Find the share of A.

Solution:

From both the ratios

Sum of first ratio = 3 + 8 = 11

Sum of second ratio = 2 + 5 = 7 

LCM of 11 and 7 = 77 

Let A + B + C = 77 unit

Multiplying by 7 in first ratio; 

​$$\frac{C}{A+B}= \frac{3 ×7}{8×7} = \frac{21}{56}$$ 

​Multiplying by 11 in first ratio; 

​$$\frac{B}{A+C}= \frac{2\times 11}{5\times 11} = \frac{22}{55}$$ 

We get the value of  B = 22 and C = 21

so, A = 77 -( 21 + 22) = 77 - 43 = 34 

Now, 

Share of A = $$\frac{9240}{77} \times 34 = ₹4080$$​​

Alternate Solution (Exam Trick):