P pays Q a sum of Rs 150 using coins of Rs 2, Rs 5, and Rs 10. He uses a total of 50 coins. If the ratio of Rs 2 and Rs 5 coins used is 5 : 2, then how many coins of Rs 10 are used in the payment?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1.
Let
The number of Rs 2 coins = 5x.
The number of Rs 5 coins = 2x.
The number of Rs 10 coins = z.
The total number of coins used is 50:
5x + 2x + z = 50
⇒ z = 50 - 7x ---- (1)
The total amount paid is Rs 150:
⇒ 2(5x) + 5(2x) + 10z = 150
⇒ 10x + 10x + 10z = 150
⇒ 20x + 10z = 150
From Equation 1:
Substitute z = 50 − 7x
⇒ 20x + 10(50−7x) = 150
⇒ 20x + 500 − 70x = 150
⇒ −50x + 500 = 150
⇒ −50x = 150 − 500
⇒ −50x = −350
⇒ x = 7
Put x = 7 in Equation 1:
z = 50 − 7(7) = 50 − 49 = 1
The number of Rs 10 coins used is 1.