Form the pair of linear equations for the following problems and find their solution by substitution method.
The difference between two numbers is 26 and one number is three times the other. Find them.
The two numbers are 39 and 13.
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
The two supplementary angles are 99° and 81°.
The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. Later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball.
Cost of each bat = ₹ 500, Cost of each ball = ₹ 50.
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
Fixed charge = ₹ 5, Charge per km = ₹ 10, Total charge for 25 km = ₹ 255.
A fraction becomes , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes . Find the fraction.
The fraction is 7/9.
Explanation
This question tests the student's ability to formulate linear equations from word problems and solve them using the substitution method as explained in Section 3.3.1 of the textbook. Students must identify variables, form equations based on given conditions, substitute one variable into another equation, and solve systematically.