Class 10 - Chapter 3: Linear Equations

Section A (1 Mark each)

Q1. The sum of two numbers is 27 and their difference is 5. The numbers are:

(a) 15, 12 (b) 17, 10 (c) 16, 11 (d) 14, 13

Q2. A father is 3 times as old as his son. After 12 years, his age will be twice as that of his son. The present age of the son is:

(a) 10 years (b) 12 years (c) 15 years (d) 18 years

Q3. In a cyclic quadrilateral ABCD, $\angle A = (x + y + 10)^\circ$, $\angle B = (y + 20)^\circ$, $\angle C = (x + y - 30)^\circ$ and $\angle D = (x + y)^\circ$. Then $y = $

(a) 40 (b) 30 (c) 20 (d) 10

Q4. Assertion (A): If the pair of linear equations $3x + 2y = 12$ and $2x + 3y = 13$ represent the cost of pens and notebooks, then the cost of one pen is ₹ 2.
Reason (R): Solving the equations gives $x = 2$ and $y = 3$.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Solve on white paper.

Q6. A fraction becomes $\frac{9}{11}$ if 2 is added to both the numerator and the denominator. If 3 is added to both, it becomes $\frac{5}{6}$. Find the fraction.

Solve on white paper.

Q7. 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.

Solve on white paper.

Section C (3 Marks each)

Q8. 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 7 days, while Susy paid ₹ 21 for the book she kept for 5 days. Find the fixed charge and the charge for each extra day.

Solve on white paper.

Q9. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Solve on white paper.

Section D (5 Marks)

Q10. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Hostel Charges

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges.

(i) Formulate the pair of linear equations representing the situation.

(ii) Find the fixed charge.

(iii) Find the cost of food per day.

Solve on white paper.