Question

A gives B as many rupees as B has and C as many rupees as C. Similarly, B then gives A and C as many rupees as each then has C. similarly, C then gives A and B as many rupees as each then has. If each person finally has 16 rupees with how many rupees does A start?
A. 26
B. 28
C. 30
D. 32

Answer 1

Hint: Here we have to solve the problem in a reverse way. It is mentioned that each has 16 rupees at the end. So with each of the given conditions, we have to find the total amount initially A had.

Complete step by step solution:
Given that at the end A, B and C has 16 rupees each.

Step I
It is mentioned that C gave A and B as many rupees as each of them has.
So dividing the amount of rupees A and B has by half.
Therefore before C gave money, A had
$\begin{array}{c} = \dfrac{{16}}{2}\\ = 8\;{\rm{rupees}}\end{array}$
Similarly, B has
$\begin{array}{c} = \dfrac{{16}}{2}\\ = 8\;{\rm{rupees}}\end{array}$
Since, C gave the same amount as A and B already they had.
Therefore C gave 8 rupees to A and 8 rupees to B.
Thus, before giving to A and B, C has
$\begin{array}{l} = 16 + 8 + 8\\ = 32\;{\rm{rupees}}\end{array}$

Step II
B gave A and C as many rupees as each of them has.
So dividing the amount of rupees A and C has by half.
Therefore before C gave money, A had
$\begin{array}{c} = \dfrac{8}{2}\\ = 4\;{\rm{rupees}}\end{array}$
Similarly B has
$\begin{array}{c} = \dfrac{{32}}{2}\\ = 16\;{\rm{rupees}}\end{array}$
Since, B gave the same amount as A and C already they had.

Therefore B gave 4 rupees to A and 16 rupees to C.
Thus, before giving to A and C, B has
$\begin{array}{l} = 4 + 8 + 16\\ = 28\;{\rm{rupees}}\end{array}$

Step III
A gave B and C as many rupees as each of them has.
So dividing the amount of rupees B and C has by half.
Therefore before A gave money, B had
$\begin{array}{c} = \dfrac{{28}}{2}\\ = 14\;{\rm{rupees}}\end{array}$
Similarly C has
$\begin{array}{c} = \dfrac{{16}}{2}\\ = 8\;{\rm{rupees}}\end{array}$
Since, A gave the same amount as B and C already they had.

Therefore, A gave 14 rupees to B and 8 rupees to C.
Thus, before giving to B and C, A has
$\begin{array}{l} = 4 + 14 + 8\\ = 26\;{\rm{rupees}}\end{array}$
Thus, initially A has 26 rupees.

Hence, the correct option (a).

Note: Here we have to determine the total amount of money initially A has. Since the total money A, B and C at the end are given, we can easily calculate the amount of money that A has by simplifying the data according to the given conditions.