A payment of ₹120 is made with ₹10, ₹5 and ₹2 coins. A total of 25 coins are used. Which of the following is the number of ₹10 coins used in the payment?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 5.
Let the number of ₹10 coins, ₹5 coins, and ₹2 coins be x, y, and z respectively
So,
Total payment = 10x + 5y + 2z = 120....(a)
Total coins = x + y + z = 25....(b)
⇒ z = 25 - x - y
Now,
⇒ 10x + 5y + 2(25 - x - y) = 120
⇒ 10x + 5y + 50 - 2x - 2y = 120
⇒ 8x + 3y = 70....(1)
⇒ y = (70 - 8x)/3
Let the value of x = 5
⇒ y = (70 - 8x)/3
⇒ y = (70 - 8 × 5)/3
⇒ y = (70 - 40)/3
⇒ y = 30/3
⇒ y = 10
and, z = 25 - x - y
⇒ z = 25 - 5 - 10
⇒ z = 25 - 15
⇒ z = 10
Verifying by putting the values in eq a and eq b
⇒ 10x + 5y + 2z = 120....(a)
⇒ 10 × 5 + 5 × 10 + 2 × 10 = 120
⇒ 50 + 50 + 20 = 120
⇒ 120 = 120
Now,
⇒ x + y + z = 25....(b)
⇒ 5 + 10 + 10 = 25
⇒ 25 = 25
Hence,
The number of ₹10 coins used is 5