Question

Four people A, B, C, and D have together got Rs. 100 with them. A and B have got as much money as C and D put together. A has got more money than B. C has got half as money as D has. A has Rs. 5 more than D. How much money does B have?
A. 11.66
B. 13.50
C. 32.30
D. 10.30

Answer 1

Hint: To solve this question, we will first assume the money A, B, C, and D have to be a, b, c, and d. Then we will use the given relations between the money they have, i.e. a, b, c, and d, and form as much as equations we can in these 4 variables. Then, we will solve these equations and try to obtain a required value for b. Thus, we will get the required answer.

Complete step-by-step solution
Now, to find the money B has, we will first assume the money A, B, C, and D have to be a, b, c, and d.
Now, we have been given that all of them together have Rs. 100 with them. Thus, we get:
$a+b+c+d=100$ .....(ii)
We have also been given that A and B have got as much as money as C and D have put together. Thus, we can say that:
$a+b=c+d$ .....(i)
Now, putting equation (ii) in equation (i) we get:
$\begin{align}
  & a+b+c+d=100 \\
 & \Rightarrow a+b+a+b=100 \\
 & \Rightarrow 2\left( a+b \right)=100 \\
\end{align}$
$\Rightarrow a+b=50$ …..(iii)
Now, since $a+b=c+d$, we get:
$c+d=50$ .....(iv)
Now, we have been given that A has more money than B.
Thus, we get:
$a>b$
We have also been given that C has got half as money as D. Thus, we can say that:
$c=\dfrac{d}{2}$
Thus, putting the value of c in equation (iv) we get:
$\begin{align}
  & c+d=50 \\
 & \Rightarrow \dfrac{d}{2}+d=50 \\
 & \Rightarrow \dfrac{3d}{2}=50 \\
 & \Rightarrow d=\dfrac{100}{3} \\
\end{align}$
Now, we have been given that A has Rs. 5 more than D. Thus, we can say that:
$a=d+5$ .....(v)
Now, putting the value of d in equation (v) we get:
$\begin{align}
  & a=d+5 \\
 & \Rightarrow a=\dfrac{100}{3}+5 \\
 & \Rightarrow a=\dfrac{100+15}{3} \\
 & \Rightarrow a=\dfrac{115}{3} \\
\end{align}$
Now, putting this value of a in equation (iii), we get:
\[\begin{align}
  & a+b=50 \\
 & \Rightarrow \dfrac{115}{3}+b=50 \\
 & \Rightarrow b=50-\dfrac{115}{3} \\
 & \Rightarrow b=\dfrac{150-115}{3} \\
 & \Rightarrow b=\dfrac{35}{3} \\
\end{align}\]
Now, converting the value of b in decimals, we get:
$\begin{align}
  & b=\dfrac{35}{3} \\
 & \therefore b=11.66 \\
\end{align}$
Thus, B has Rs. 11.66
Hence, option (A) is the correct option.

Note: Here, we have kept all these values in the fractional form until the end to make calculations easier and decrease the scope for mistakes, and also making the answer as much as accurate as it can be. We also could have kept them in the decimal form when we obtained the first fractional form and solved the question like that but it may have increased the scope for mistakes or decreased the accuracy of the answer.