NCERT Mathematics Class 10 Exemplar Ch 3 Pair of Linear Equations in Two Variables Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Graphically, solve the following pair of equations: and Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.


2. Determine, graphically, the vertices of the triangle formed by the lines


3. Draw the graphs of the equations and . Also find the area of the quadrilateral formed by the lines and the x – axis.

Answer: 8 sq. units

4. The cost of 4 pens and 4 pencil boxes is ₹ 100. Three times the cost of a pen is ₹ 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

Answer: , , where ₹ x and ₹ y are the costs of a pen and a pencil box respectively; ₹ 10, ₹ 15

5. Determine, algebraically, the vertices of the triangle formed by the lines and


6. Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.

Answer: ,

7. A person, rowing at the rate of in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.


8. A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Answer: ,

9. A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Answer: 83

10. A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs ₹ 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs ₹ 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.

Answer: ₹ 2500, ₹ 30

11. A shopkeeper sells a saree at 8 % profit and a sweater at 10 % discount, thereby, getting a sum ₹ 1008. If she had sold the saree at 10 % profit and the sweater at 8 % discount, she would have got ₹ 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.

Answer: ₹ 600, ₹ 400

12. Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8 % per annum and 9 % per annum, respectively. She received ₹ 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received ₹ 20 more as annual interest. How much money did she invest in each scheme?

Answer: ₹ 12000 in scheme A, ₹ 10000 in scheme B

13. Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of ₹ 2 for 3 bananas and the second lot at the rate of Re 1 per banana, and got a total of ₹ 400. If he had sold the first lot at the rate of Re 1 per banana, and the second lot at the rate of ₹ 4 for 5 bananas, his total collection would have been ₹ 460. Find the total number of bananas he had.

Answer: 500