Question

The sum of Rs 750 is distributed among A, B, C and D in such a manner that A gets as much as B and C together, B gets Rs 125 more than C, D gets as much as C. What is A’s share?
$
  {\text{A}}{\text{. Rs 100}} \\
  {\text{B}}{\text{. Rs 225}} \\
  {\text{C}}{\text{. Rs 275}} \\
  {\text{D}}{\text{. Rs 325}} \\
 $

Answer 1

Hint: Here, we will proceed by assuming D’s share as a variable and then representing A’s share, B’s share, C’s share in terms of the variable assumed for D’s share and then we will obtain an equation in this variable according to the problem statement.

Complete Step-by-Step solution:
Let D’s share be x
Given, D’s share is same as that of C’s share i.e., C’s share = D’s share
$ \Rightarrow $C’s share = x
Also given that B’s share is Rs 125 more than C’s share i.e., B’s share = C’s share + 125
$ \Rightarrow $B’s share = x+ 125
Also given that A’s share is equal to the sum of B’s share and C’s share i.e., A’s share = B’s share + C’s share
$ \Rightarrow $A’s share = (x+ 125) + x
$ \Rightarrow $A’s share = 2x + 125
Since, Rs 750 is divided into A’s share, B’s share, C’s share and D’s share
i.e., A’s share + B’s share + C’s share + D’s share = 750
 $ \Rightarrow $(2x+125) + (x+125) + x + x = 750
 $ \Rightarrow $5x+250 = 750
$ \Rightarrow $5x = 500
$ \Rightarrow $ x = $\dfrac{{500}}{5}$ = 100
i.e., D’s share = C’s share = x = Rs 100
B’s share = x+125 = 100+125 = Rs 225
A’s share = 2x+125 = 2(100) + 125 = 200 + 125 = Rs 325
Therefore, A’s share is Rs 325.
Hence, option D is correct.

Note: In this particular problem, we have used only one variable i.e., D’s share = x instead of assuming four variables corresponding to each A’s share, B’s share, C’s share and D’s share in order to avoid unnecessary calculations. In that case where four variables are considered we need to obtain at least four equations in order to solve these.