Question

Arvind has a piggy bank. It is full of one-rupee and fifty paise coins. It contains 3 times as many fifty paise coins as one rupee coins. The total amount of money in the bank is Rs 35. How many one-rupee and fifty paise coins are in the bank? (respectively)
(a) 14, 42
(a) 15, 42
(a) 14, 52
(d) None of these

Answer 1

Hint: In order to solve this problem, we need to find the proper mathematical equation for the condition given in the question. Summing the total number of coins according to their respective values and equating to Rs 35 we can get the number of coins of each type.

Complete step-by-step answer:
We have two types of coins, fifty paise and one rupee coins.
We need to know the relation that 100 paise means one rupee.
It can also be said as two fifty paise coins make one rupee.
According to the condition, we have been told that Arvind has 3 times as many fifty paise coins as one rupee coins.
This means that the quantity of fifty paise coins is thrice than that of one rupee coins
Let the number of 1 rupee coin be $x$ .
According to the condition number of 50 paise coins will be $3x$ .
The value of a one-rupee coin is twice that of 50 coins.
We can also say that the value of 50 paise coin is half than that of one-rupee coin
As it is given in the question that total money in the bank is Rs 35.
Therefore, by formulating the equation we get,
$0.5\left( 3x \right)+x=35$
Solving the equation for $x$ we get,
$\begin{align}
  & 1.5x+x=35 \\
 & 2.5x=35 \\
 & x=\dfrac{35}{2.5}=14.............(i) \\
\end{align}$
Therefore, the number of one rupee coins are 14 and the number of 50 paise coins are $3x=3\times 14=42$ coins.
Hence option (a) is the correct option.

Note: We can see that the number of fifty paise coins are thrice of the one rupee coins so we can eliminate two of the options (B) and (C) as they are not thrice. Also, it is easily confused with the condition statement. The common mistake is taking the number of fifty paise coins as thrice than that of one wrong rupee coin. It is very important to read the question very carefully.