CHALLENGING PROBLEMS CLASS X MODULE 1
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This document contains 10 challenging math problems involving linear and quadratic equations. The problems cover a range of topics including ages, train speeds, rectangular areas, filling pools with pipes, ticket prices, selling bananas, combined transportation times using rickshaws and buses, and boat speeds upstream and downstream. The student is asked to solve each of the 10 problems presented.
CHALLENGING PROBLEMS CLASS X MODULE 1
- 1. CHALLENGING PROBLEMS MISHAL CHAUHAN STHITPRAGYA SCIENCE CLASSES, GANDHIDHAM CLASS 10 MODULE – 1
- 2. 10 PROBLEMS ON LINEAR AND QUADRATIC EQUATIONS
- 3. QUESTION – 1 If Zara were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
- 4. QUESTION – 2 At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
- 5. QUESTION – 3 A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
- 6. QUESTION – 4
- 7. QUESTION – 5 In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2. Find the length and breadth of the pond.
- 8. QUESTION – 6 It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. How long would it take for each pipe to fill the pool separately?
- 9. QUESTION – 7 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 Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.?
- 10. QUESTION – 8 Vijay had some bananas,and he divided them into Twp 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. .?
- 11. QUESTION – 9 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.
- 12. QUESTION – 10 A person, rowing at the rate of 5 km/h 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.
- 13. Good luck….