Question

In a bag, there are coins of 50 paise, 25 paise and 1 rupee in the ratio of 5: 6: 2. If there are in all Rs. 42 in the bag how many coins of 25 paise does the bag have?
A) 42
B) 21
C) 15
D) 16

Answer 1

Hint: For solving this question, the ratios of the coins are given. We let the number of coins in terms of ‘x’ like 5x, 6x and 2x individually. On adding all the prices of coins in terms of x and putting them equals to 42 rupees, we get the value of x and we easily find the total number of 25 paise coins.

Complete step-by-step answer:
Let, total number of 50 paise coins be 5x.
We know that 1 rupee = 100 paise. Using this we convert paise into rupees.
Converting 50 paise into rupees =$\dfrac{50}{100}\times 5x=\dfrac{5x}{2}$
Total number of 25 paise be 6x.
Converting 25 paise into rupees =$\dfrac{25}{100}\times 6x=\dfrac{3x}{2}$
And the total number of 1-rupee coins will be 2x.
Now adding all the price of coins and putting equal to total number of rupees in the bag, we get
Total rupees in the bag = price of 50 paise coins + price of 25 paise coins + price of 1-rupee coins
  $42=\dfrac{5x}{2}+\dfrac{3x}{2}+2x$
Taking L.C.M in the right-hand side, we get
$\begin{align}
  & 42=\dfrac{5x+3x+4x}{2}=\dfrac{12x}{2} \\
 & 42=6x \\
 & x=\dfrac{42}{6} \\
 & x=7 \\
\end{align}$
Hence, the total 25 paise coins is 6x, = $6\times 7=42$.
Therefore, option (a) is correct.

Note: An important step in solving this problem is the conversion of given currency into a standard currency. Since the total price is given in rupees, all the currencies are converted in rupees. A common mistake occurs when a student ignores the currency pair.