Question

In a fair, Megha and Meena spent rupees 95 altogether. Meena and Tia pant rupees 216 altogether. If Meena spent one fifth of what Tia spent, how much did Megha spend?
(a) Rs. 59
(b) Rs. 65
(c) Rs. 70
(d) Rs. 79

Answer 1

Hint: In this problem, we let the money spent by Tia be x. Now, by using the last statement we obtain the money spent by Meena. Both Meena and Tia spent 216 rupees so by using the above part we calculate the money spent by Tia and Meena individually. Now, we can easily find the amount of money spent by Megha.

Complete step-by-step answer:
According to the question, we are given that,
Amount of money spent by Meena in the fair is one-fifth of the amount Tia spent in the same fair.
Also, in the second statement of problem, the amount of money Meena and Tia spend altogether = Rs.216.
Now, by using both the statement, we conclude that one-fifth of amount of money Tia spent + Amount of money Tia spent in the fair = Rs.216
\[\therefore \left( \dfrac{1}{5}+1 \right)\] of amount of money Tia spent in fair = Rs. 216.
 Let, the amount of money Tia spent be x.
Therefore, above statement can be reduced to:
$\begin{align}
  & \dfrac{6}{5}x=216 \\
 & x=216\times \dfrac{5}{6} \\
 & x=180 \\
\end{align}$
Amount of money spent by Tia in the fair individually is Rs. 180.
So, the amount of money Meena spent $=\dfrac{1}{5}x=\dfrac{1}{5}\times 180=36$.
Amount spent by Meena in fair = Rs. 36
Now, amount of money Megha and Meena spent altogether = Rs.95
Amount of money Megha spent =Rs. (95 – 36) = Rs.59.
Therefore, option (a) is correct.

Note: The key step for solving this problem is the manipulation of data by using the problem statement. Our target in these questions is to identify the main person around whom all the data revolves. Like in this case by letting Tia’s spending as x, we obtain all the spending. This knowledge is useful for solving complex problems.