Question

A and B each has some money. If A gives Rs 30 to B then B will have twice the money left with A. But if B gives Rs 10 to A then A will have thrice as much as is left with B. How much money does each have?
a) 62, 34
b) 60, 34
c) 60, 36
d) 62, 30

Answer 1

Hint: Take the amount with A and B as ‘x’ and ‘y’ with the given conditions formulate two expressions with x and y. Now, we can start using the first condition, A given 30 to B, then B will have twice money left with A. So, we can express it as
$y+30=2\left( x-30 \right)$

Complete step-by-step answer:
Let us consider the money A as ‘x’ and the amount with B as ‘y’. It is said that A gives Rs 30 to B, then B will have twice the money as that of A. Thus let us form the expression with the given information $\left( y+30 \right)$ is the money with B after A gives Rs 30. At the same time A loses Rs 30, thus $\left( x-30 \right)$ Hence we can say that $y+30=2\left( x-30 \right)$ as the money with B is twice that of A.
$\begin{align}
  & y+30=2x-60 \\
 & \Rightarrow 2x-y=90 \\
 & \therefore y=2x-90...................\left( 1 \right) \\
\end{align}$
Now it is said that B givens Rs 10 to A and then A will have thrice as much as B. $\left( x+10 \right)$ is the money with A after B gives Rs 10 to A. Now the money with B is $\left( y-10 \right)$ . Hence we can form the expression as
$x+10=3\left( y-10 \right)$
As the money with A is thrice that of the remains of B. Let us simplify it as
$\begin{align}
  & x+10=3y-30 \\
 & x=3y-40......................\left( 2 \right) \\
\end{align}$
Let us put the value of (2) in (1)
$\begin{align}
  & y=2x-90 \\
 & y=2\left( 3y-40 \right)-90 \\
 & \Rightarrow y=6y-80-90 \\
 & 5y=170 \\
 & \therefore y=34 \\
\end{align}$
Now put $y=34$ in equation (2)
$x=3\times 34-40=102-40=62$
Thus we got the amount with A = x = Rs 62.
The money with B = y = Rs 34.
Thus we get the money with A = Rs 62 and B = Rs 34.
Therefore option (a) is the correct answer.

Note: While forming the ${{2}^{nd}}$ set of expression don’t consider the ${{1}^{st}}$ case where A gives Rs 30. Both are 2 different cases considering the exchange of money between A and B. So read the question carefully before formulating the expressions. In order to solve the equations we could also have used the elimination method as an alternative.