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
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.
– 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.