Question

Aravind has a kiddy 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 the money in the bank is Rs.35. How many coins of each kind are there in the bank?

Answer 1

Hint: First of all, consider the number of one-rupee coins as a variable and then find the number of fifty paise coins in terms of one-rupee coins by the given condition. Then equate the amount of one-rupee coins and fifty-rupee coins to the total given amount.

Complete step-by-step answer:

Let the number of one-rupee coins be \[x\]
Since the kiddy bank contains 3 times as many fifty paise coins as one-rupee coins the number of 50 paise coins are \[3x\].
Let \[S\]be the total amount in the kiddy bank i.e., \[S = {\text{Rs}}{\text{.35}}\]
The amount of one-rupee coins in the kiddy bank \[ = x \times {\text{Rs}}{\text{.1}} = {\text{Rs}}{\text{.}}x\]
And the amount of fifty paise coins in the kiddy bank \[ = 3x \times {\text{Rs}}{\text{.}}\dfrac{1}{2} = {\text{Rs}}{\text{.}}\dfrac{{3x}}{2}\]
So, we have
\[
   \Rightarrow S = x + \dfrac{{3x}}{2} \\
   \Rightarrow 35 = \dfrac{{2x + 3x}}{2} \\
   \Rightarrow 5x = 35 \times 2 \\
   \Rightarrow x = \dfrac{{70}}{5} \\
  \therefore x = {\text{Rs}}.14 \\
\]
Since \[x = 14\], we have \[3x = 3\left( {14} \right) = 42\]
Hence, there are 14 one-rupee coins and 42 fifty paise coins in the kiddy bank.

Note: In the solution the value of \[x\] cannot be negative. And the number of obtained fifty-rupee coins must be greater than the number of obtained one-rupee coins. The total number of coins in the kiddy bank = 14 + 42 = 56.