P pays Q a sum of ₹150 using coins of ₹2, ₹5 and ₹10. He uses a total of 50 coins. If the ratio of ₹2 and ₹5 coins used is 5 : 2, then how many coins of ₹10 are used in the payment?
P pays Q a sum of ₹150 using coins of ₹2, ₹5 and ₹10. He uses a total of 50 coins. If the ratio of ₹2 and ₹5 coins used is 5 : 2, then how many coins of ₹10 are used in the payment?
P, Q को ₹2, ₹5 और ₹10 के सिक्कों का उपयोग करके ₹150 का भुगतान करता है। वह कुल 50 सिक्कों का उपयोग करता है। यदि उपयोग किए गए ₹2 और ₹5 के सिक्कों का अनुपात 5:2 है, तो भुगतान में ₹10 के कितने सिक्के उपयोग किए गए?
Detailed Solution & Logic
Correct Answer:
1
Given:
₹2 and ₹5 coins are in the ratio 5 : 2
Let number of ₹2 coins = 5x
Let number of ₹5 coins = 2x
Let number of ₹10 coins = y
Step 1: Total coins
5x + 2x + y = 50
7x + y = 50
Step 2: Total amount
2(5x) + 5(2x) + 10y = 150
10x + 10x + 10y = 150
20x + 10y = 150
Divide by 10:
2x + y = 15
Step 3: Solve equations
7x + y = 50
2x + y = 15
Subtract:
5x = 35 ⇒ x = 7
Now, y = 15 − 2x = 15 − 14 = 1
Final Answer: 1
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