Question

For 240 coins in the box, contains coins of 50 paisa, 1 rupee and 2 rupees. The value of each kind of coin is in the ratio 8:7:15 respectively. How many 1-rupee coins there in the box?
A. 48
B. 90
C. 102
D. 108

Answer 1

Hint: The box coins the 50 paisa coins, 1-rupee coins and last the contain 2-rupee coins also. The ratio of all three coins as per the question is 8:7:15. First we find the ratio of all 3 coins with respect to the ratio of the total number of coins in the box. Then we find the number of 1-rupee coins in the box by multiplying the total number of coins i.e. 240 and finally the ratio of one-rupee coins with respect sum of the ratio of all three coins. Hence, we get the answer at last.

Complete step-by-step answer:
The ratio of 50 paise coins: ratio of 1-rupee coins: ratio of 2-rupees is 8:7:15. This ratio is part to part ratio for holding the exact number of coins of each group. We need to convert the ratio in part to whole and multiply with the total number of coins,
The ratio of 50 paise coins and total number of coins are given by:
50 paisa: total number of coins$=\dfrac{8}{8+17+15}=\dfrac{8}{40}$.
The ratio of 1-rupee coins and total number of coins are given by:
1-rupee coins: total number of coins$=\dfrac{17}{8+17+15}=\dfrac{17}{40}$.
The ratio of 2-rupee coins and the total number of coins are given by:
2-rupee coins: total number of coins$=\dfrac{15}{8+17+15}=\dfrac{15}{40}$.
Now, we are required to find out the total number of coins of 1 rupee,
Total number of 1-rupee coins$=240\times \dfrac{17}{40}$.
Total number of 1-rupee coins$=6\times 17=102$.
Hence, the total number of coins of 1 rupee are 102.
Therefore, option (c) is correct.

Note: The key step for solving this problem is the expression of the individual currency pair with total number of coins. By doing so we get the exact number of coins for the particular denomination. At the core, it is a problem of ratio and proportion disguised in the language of currency and should be solved keeping the same in mind.