A person has a total of 100 coins consisting of ₹ 2 and ₹ 5 coins. If

A person has a total of 100 coins consisting of ₹ 2 and ₹ 5 coins. If the total value of the coins is ₹ 320, then the number of ₹ 2 coins is

[amp_mcq option1=”40″ option2=”50″ option3=”60″ option4=”70″ correct=”option3″]

This question was previously asked in
UPSC CAPF – 2022
Let x be the number of ₹ 2 coins and y be the number of ₹ 5 coins.
We are given two pieces of information:
1. The total number of coins is 100: x + y = 100
2. The total value of the coins is ₹ 320: 2x + 5y = 320
We have a system of two linear equations with two variables. We want to find the value of x.
From the first equation, we can express y as y = 100 – x.
Substitute this into the second equation:
2x + 5(100 – x) = 320
2x + 500 – 5x = 320
500 – 3x = 320
500 – 320 = 3x
180 = 3x
x = 180 / 3 = 60.
So, there are 60 coins of ₹ 2.
If x = 60, then y = 100 – 60 = 40.
Check the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct.
– Set up a system of linear equations based on the problem statement.
– One equation represents the total count of items.
– Another equation represents the total value based on the count and individual item values.
– Solve the system of equations using substitution or elimination to find the required variable.
This is a standard word problem that translates into a system of linear equations, often encountered in basic algebra and quantitative aptitude tests. The variables represent the counts of different denominations, and the equations represent the total count and the total value.