Question

Three persons A, B and C had Rs. 360 altogether. A transferred half of the amount he had to B and C transferred half of the amount he had to A. After the transfer, all of them have equal amounts. What is the total amount B had before the transfer?
1. Rs. 0
2. Rs. 180
3. Rs.  120
4. Rs. 240

Answer 1

Correct Answer - Option 3 : Rs.  120

Given,

Three persons A, B, and C had Rs. 360 altogether.

A transferred half of the amount he had to B and C transferred half of the amount he had to A.

After the transfer, all of them have equal amounts.

Therefore, A + B + C = 360 at the end they have 120 each.

Final amount of A = Final amount of B = Final amount of C = 120

Let 2y be the initial amount with C.

Then amount given by C to A = y

Final amount of C = 120 = inital amount of C - amount transferred to A = 2y - y = y

Therefore, y = 120.

Therefore, initial amount of C must be 240 and amount transferred to A = 120.

So, initially, A + B = 120 because A + B + C = 360.

Now, final amount of B = 120 and before transfer A + B = 120........ (I)

Let 2x be the amount with A initially and z be the initial amount with B.

Then 2x + z = 120. (from I) ..........(1)

Also, x + z = 120 (amount transferred by A + initial amount of B = final amount of B)  .............(2)

From (1) and (2), we get 2x + z = x + z.

⇒ 2x = x

⇒ x = 0 and z = 120.

Hence, B had Rs. 120 initially.