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Class 10 Word Problems on Linear Pairs — practice questions with answers

Algebra — Systems of Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The sum of two numbers is 20 and their difference is 4. What is the larger number?
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Answer: A) 12
Let numbers be x and y. x + y = 20, x - y = 4. Adding: 2x = 24, x = 12.
2. In an examination Rohan got 40 marks by answering some questions. He gets 3 marks for each correct answer and loses 1 mark for each wrong answer. He attempted 20 questions in total. How many did he answer correctly?
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Answer: A) 15
c + w = 20, 3c - w = 40. Adding: 4c = 60, c = 15.
3. Two trains start at the same time from stations P and Q, 300 km apart, moving towards each other. They meet after 2 hours. If one train travels 10 km/h faster than the other, find the speed (in km/h) of the slower train.
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Answer: A) 70 km/h
Combined speed = = 150 km/h. x + (x+10) = 150 -> 2x = 140 -> x = 70.
4. A courier company charges a fixed booking fee for a parcel plus a rate for every kilogram it weighs. A 5 kg parcel costs Rs 410 and an 8 kg parcel costs Rs 590. Find the rate (in Rs) charged per kilogram.
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Answer: D) 60
Let the booking fee be Rs x and the rate Rs y per kg. x + 5y = 410 and x + 8y = 590. Subtracting: 3y = 180, so y = 60 and x = 410 - 300 = 110. Check: 110 + 8 x 60 = 590. 110 is the booking fee, the other unknown; 82 comes from dividing the whole 5 kg charge by 5, which wrongly spreads the booking fee over the weight; 180 is the difference between the two charges before dividing by the 3 kg.
5. A sum of Rs 15000 is deposited in two banks. Bank A pays 7% and Bank B pays 9% simple interest per year. After one year the interest from Bank B is Rs 390 more than the interest from Bank A. How much (in Rs) was deposited in Bank A?
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Answer: D) 6000
Let Rs x go to Bank A and Rs y to Bank B. x + y = 15000 and 0.09y - 0.07x = 390, that is 9y - 7x = 39000. Substituting y = 15000 - x: 135000 - 9x - 7x = 39000, so 16x = 96000 and x = 6000, giving y = 9000. Check: 6000 + 9000 = 15000, and 810 - 420 = 390. 9000 is the Bank B deposit, the swapped unknown; 7500 splits the sum equally, which would give interests of 525 and 675 differing by only Rs 150; 420 is the interest Bank A pays, not the amount deposited there.
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