A sum of ₹ 6,270 is divided between A, B and C in such a way that the ratio of A's share to that of B and C combined is 3 : 7 and the ratio of B's ​​share to that of A and C combined is 2 : 9. What is C's share

Correct option is D

Given: 

A + B +C = 6270 

A : B + C = 3 : 7 

B : A + C = 2 : 9 

Solution:   

(A : B + C = 3 : 7)  = 10  Unit  ........ (i)

(B : A + C = 2 : 9 )= 11 Unit .........(ii) 

in both condition (A + B + C) value is different so we equate  

equation (i) multiply by 11 and equation (ii) multiply by 10

then,

(A : B + C = 3 : 7) x 11  = 10 x11  Unit   

A :  B + C = 33 : 77  = 110 Unit

(B : A + C= 2: 9 ) x 10=  11x10 unit 

B : A + C = 20 : 90 = 110 Unit 

A = 33 Unit , B = 20 unit C = [110 - (33+20)] = 57

According to the question 110 unit = 6270 

1 unit = $$\frac{6270}{110}$$ 

The share of C = 57 unit = 57$$\times\frac{6270}{110}$$  = Rs. 3249​