Here you get the CBSE Class 10 Mathematics chapter 3, Pair of Linear Equations in Two Variables: NCERT Exemplar Problems and Solutions (Part-IVB). This part of the chapter includes solutions of Question Number 7 to 13 from Exercise 3.4 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Pair of Linear Equations in Two Variables. This exercise comprises only of the Long Answer Type Questions framed from various important topics in the chapter. Each question is provided with a detailed solution.
NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Pair of Linear Equations in Two Variables:
Long Answer Type QuestionsQuesntion (Q. No. 7 to 13)
7. A person, rowing at the rate of 5km/h in still water, takes thrice as much time in going 40km upstream as in going 40km downstream. Find the speed of the stream.
Let the speed of the stream be x km/h.
Given, speed of person, rowing in still water = 5 km/h
The speed of a person rowing in downstream = (5 + x) km/h
and the speed of a person has rowing in upstream = (5 − x) km/h
Now, time taken to cover 40km downstream,
Hence, the speed of the stream is 2.5km/h.
Quesntion8. A motorboat can travel 30km upstream and 28km downstream in 7h. It can travel 21km upstream and return in 5h. Find the speed of the boat in still water and the speed of the stream.
Let speed of the motorboat in still water = x km/h
And speed of the stream = y km/h
Then, speed of the motorboat in downstream = (x + y) km/h
And speed of the motorboat in upstream = (x - y) km/h.
Time taken by motorboat to travel 30 km upstream,
Hence, the speed of the motorboat in still water is 10km/h and the speed of the stream is 4km/h.
Quesntion9. 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.
Let the two-digit number be = 10 x + y
Now, put the value of y in equation (i), we get
2x - 7 × 3 = -5
⟹ 2x = 21 - 5 = 16
⟹ x = 8
Hence, the required two-digit number = 10x + y = 10 × 8 + 3 = 80 + 3 = 83
Quesntion10. A railway half ticket cost 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 stations A to B costs Rs. 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations A to B costs Rs.3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.
Let cost of full class fare be Rs x
Thus cost of half first class fare = Rs. x/2 , respectively
Again let reservation charges per ticket be Rs. y.
⟹ y = 2530-2500
⟹ y = 30
Hence, full first class fare from stations A to B is Rs. 2500 and the reservation for a ticket is Rs. 30.
Quesntion11. A shopkeeper sells a saree at 8% profit and a sweater at 10% discount thereby, getting a sum Rs.1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs.1028 then find the cost of the saree and the list price (price before discount) of the sweater.
Let the cost price of the saree be Rs. x
And list price of the sweater be Rs. y.
Therefore, the cost price of the saree and the list price (price before discount) of the sweater are Rs. 600 and Rs.400.
Quesntion12. 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 Rs. 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs. 20 more as annual interest. How much money did she invest in each scheme?
Let the money invested in scheme A = Rs. x
Aand the money invested in scheme B = Rs. y
Interest at the rate of 8% per annum on scheme A+ Interest at the rate of 9% per annum on scheme B = Total amount received
Interest at the rate of 9% per annum on scheme A + Interest at the rate of 8% per annum on scheme B = Rs. 20 more than annual interest
Hence, the amount invested in schemes A and B are Rs.12000 and Rs. 10,000 respectively.
Quesntion13. Vijay had some bananas and he divided them into two lots A and B. He sold the first lot at the rate of Rs. 2 for 3 bananas and the second lot at the rate of Rs. 1 per banana and got a total of Rs. 400. If he had sold the first lot at the rate of Rs. 1 per banana and the second lot at the rate of Rs. 4 for 5 bananas, his total collection would have been Rs. 460. Find the total number of bananas he had.
Let the number of bananas in lot A = x
and the number of bananas in lot B = y
Cost of the first lot at the rate of Rs. 2 for 3 bananas + Cost of the second lot at the rate of Rs. 1 per banana = Amount received
Cost of the first lot at the rate of Rs. 1 per banana + Cost of the second lot at the rate of Rs. 4 for 5 bananas = Amount received
Hence, Total number of bananas = x + y = 300 + 200 = 500 bananas.
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