Rs. 960 were distributed among A, B, C and D in such a way that C and D

Ques - Rs. 960 were distributed among A, B, C and D in such a way that C and D together gets half of what A and B together gets and C gets one third amount of B. Also D gets 5/3 times as much as C. What is the amount of A?

(a) Rs. 240

(b) Rs. 280

(c) Rs. 320

(d) Data insifficent

Solution - 

Rs. 960 were distributed among A, B, C and D.

C + D = 1/2 (A + B)

(C + D) / (A + B) = 1/2 

And,

C = (1/3)B (given)

B/C = 3/1

B : C = 3 : 1  _______ (1)

And,

D = (5/3)C (given)

C/D = 3/5

C : D = 3 : 5  _______ (2)

From eq. 1 and eq. 2. we get,

= B : C : D

= 9 : 3 : 5

Let,

A = x

A : B : C : D = x : 9 : 3 : 5

Now,

(C + D) / (A + B) = 1/2 (given)

(3 + 5) / (x + 9) = 1/2

8 / (x + 9) = 1/2

x = 7

A + B + C + D = 7 + 9 + 3 + 5

= 24

Therefore,

The Amount of A = (x/24) × 960

= (7/24) × 960

= 7 × 40

= 280

Therefore,

The Amount of A is Rs. 280.

Hence,

The correct answer is option (b) Rs. 280.

Thank You