An amount of ₹120 is paid using ₹10, ₹5 and ₹2 coins. If the number of coins of ₹10 and ₹2 are interchanged, then the amount becomes ₹304. If the number of ₹5 and ₹2 coins are interchanged, then the amount is ₹165. How many ₹2 coins are used in the payment of ₹120?
25
Let a, b and c be the numbers of ₹10, ₹5 and ₹2 coins respectively.
Original payment: \(10a + 5b + 2c = 120\).
Interchanging the ₹10 and ₹2 counts: \(2a + 5b + 10c = 304\).
Interchanging the ₹5 and ₹2 counts: \(10a + 2b + 5c = 165\).
Subtract the first equation from the second: \(-8a + 8c = 184\), so \(c - a = 23\).
Subtract the third equation from the first: \(3b - 3c = -45\), so \(c - b = 15\).
Using \(a = c - 23\) and \(b = c - 15\) in \(10a + 5b + 2c = 120\) gives \(10(c-23) + 5(c-15) + 2c = 120\).
Expand: \(17c - 305 = 120\), so \(17c = 425\) and \(c = 25\).
Hence, the number of ₹2 coins used is 25.
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Important Questions from Linear Equation in 2 or more Variables
Six years ago, the ratio of ages of A to B was 7 ∶ 5. After 4 years from now, the ratio of their ages will be 11 ∶ 9. What is A’s age at present?
7p - [3q - {8p - (4q - 10p)}] = ?
Surya is 25 years older than his son. In 5 years, he will be twice as old as his son. What will be Surya’s age after 3 years?
The difference between the ages of two sisters is 2 years when father’s age is 52. Father is elder by 2 years to mother. Elder sister’s age is half of mother’s age. Find the age of younger sister?
The sum of the digits of a 2 digit number is 9, When 27 is added to the number, the digits get interchanged. Find the number.
A. 45
B. 36
C. 18
D. 27
