Question

A lady has 50 paise and Rs 1 coins in her purse. If in all, she has 40 coins total Rs 25.50 how many of each type of coins does she have?
A. 50paisa coin =26, 1Rs. Coin = 11
B. 50paisa coin =11, 1Rs. Coin =29
C. 50paisa coin =29, 1Rs. Coin =11
D. None of these

Answer 1

Hint: In the question we need to find the number of 50 paise coins and the number of Rs 1 coins. Assume that the number of 50 paise coins and Rs 1 coins to be variable. Formulate the linear equation in two variables using the information provided in the question by computing the number of coins on both sides of the equation. Solve these equations to get the desirable variables.

Complete step-by-step answer:
Let, x be the number of 50 paise coins and y be the number of Rs 1 coins.
In the question it is given that total coins are 40. Hence we can form the equation
⇒x+y =40 ............(i)
In the question it is given that she has totally Rs 25.50

We know that, if we multiply in 50 paisa coins and 1 Rs. Coins by corresponding their numbers of coins then we will get Rs 25.50 hence we can form equation
50 paisa can be write as \[\dfrac{1}{2}\] Rs
So, \[\dfrac{1}{2}\] Rs×( Number of 50 paise coins) + 1 Rs×( Number 1 Rs coins) = 25.5
We had already assumed,
Number of 50 paise coin = x
Number of Rs 1 coins = y
Hence we can form equation
⇒\[\dfrac{{\text{x}}}{2} + {\text{y = 25}}{\text{.5}}\]
On solving
⇒x+2y=51 ...........(ii)
Subtracting equation (i) from (ii)
⇒\[{\text{y = 11}}\]
On putting y=11 in equation (i)
⇒x=29
 Hence we get, x=29, y=11.
So Number of 50 paise coin = x = 29
Number of Rs 1 coins = y = 11
Hence option C is correct.

Note: Whenever we face such types of problems the key is to use various methods to solve the linear equation in two variables which is formed using the question’s information. The methods that can be used are elimination or substitution. In the above solution substitution is being used. This concept will help you on the right track to reach the answer.