Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes if we only add 1 to the denominator. What is the fraction?
The fraction is 3/5.
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Nuri is 50 years old and Sonu is 20 years old.
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
The two-digit number is 18.
Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.
Meena received 10 notes of ₹50 and 15 notes of ₹100.
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Fixed charge is ₹15 and charge for each extra day is ₹3.
Explanation
This question tests the student's ability to formulate a pair of linear equations from word problems and solve them using the elimination method. The elimination method involves making coefficients of one variable equal and then adding or subtracting equations to eliminate that variable.