Question

Priya has two 5-paisa coins more than the number of 25-paisa coins. The total value of the coins was Rs. 1.60. How many coins of each denomination does she have?

Answer 1

$\large\underline{\sf{Solution-}}$

It is given that number of 5-paisa coins are 2 more than the number of 25-paisa coins.

So,

Let assume that,

• Number of 25 - paisa coin be 'x'

Then

• Number of 5 - paisa coin be 'x + 2'.

So,

• Total value of 25 paisa coin = 25x paisa

• Total value of 5 paisa coin = 5(x + 2) = 5x + 10 paisa.

According to statement,

The total value of the coins was Rs. 1.60 = 160 paisa.

$\rm :\longmapsto\:25x + 10 + 5x = 160$

$\rm :\longmapsto\:30x + 10 = 160$

$\rm :\longmapsto\:30x = 160 - 10$

$\rm :\longmapsto\:30x = 150$

$\bf\implies \:x = 5$

Thus,

• Number of 25 - paisa coin = 5

• Number of 5 - paisa coin = 5 + 2 = 7

Verification :-

Number of 25 - paisa coin = 5

Then

Number of 5 - paisa coin = 7

So, Total value = 25 × 5 + 5 × 7 = 125 + 35 = 160 paisa

Hence, Verified

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in the problem.

• Understand what you have to find.

2. Translate the problem to an equation.

• Assign a variable to represent the unknown.

• Clearly mention what the unknown variable represents.

3. Carry out the plan and solve the problem.