Question

A coin box contains 50 paise and 1 rupee coins. The total number of coins is 36. The total value of 50 paise coins equals the total value of rupee coins. What is the amount in the box?

Answer 1

Hint: It is a word problem, related to the denomination of currency. To solve the problem let the number of coins of each denomination be different variables.Say 50 paisa coin be x and 1 rs coin be y.

Complete step-by-step answer:
To start with the solution, we let the number of 50 paise coins be x, and the number of 1 rupee coins be y.
It is given in the question that the box consists of a total of 36 coins, and it is also given that the value of rupee coin is equal to the value of paise coins.
From the question, we can deduce that the sum of x + y, which gives the total number of coins is equal to 36.
$\therefore x+y=36...........(i)$
Also, it is given that the total value of 50 paise i.e. $\dfrac{1}{2}rupee$ coins is equal to the total value of 1 rupee coin. Therefore, we can say:
$\dfrac{1}{2}\times x=1\times y$
Substituting the value of y from the above result in equation (i), we get
$x+\dfrac{1}{2}x=36$
$\Rightarrow \dfrac{3}{2}x=36$
$\Rightarrow x=24$
Therefore, y is equal to half of x i.e., 12.
So, the total amount is equal to $\dfrac{1}{2}\times x+1\times y=12+12=24$rupee. Therefore, the total amount in the box is Rs. 24.

Note: Don’t make a calculation error or conversion error while solving the question. Also, be sure that you convert both the denominations in the same unit, i.e., either to rupee or to paise , whichever you are comfortable in.