Class 9 Word Problems — practice questions with answers
Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The cost of a pen is Rs x and the cost of a pencil is Rs y. Write a linear equation for: 'The cost of a pen is Rs 5 more than the cost of a pencil.'
Ax = y + 5
Bx = y - 5
Cx + y = 5
Dy = x + 5
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Answer: A) x = y + 5
Pen cost is 5 more than pencil cost, so x = y + 5.
2. A cricket ball costs Rs x and a tennis ball costs Rs y. 'Two cricket balls and one tennis ball cost Rs 250.' Write the equation.
A2x + y = 250
Bx + 2y = 250
C2x + 2y = 250
Dx + y = 250
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Answer: A) 2x + y = 250
Two cricket balls = 2x, one tennis ball = y: 2x + y = 250.
3. A two-digit number has tens digit x and units digit y. Write the value of the number.
A10x + y
Bx + 10y
C10(x + y)
Dxy
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Answer: A) 10x + y
A two-digit number = 10(tens digit) + units digit = 10x + y.
4. Sunita is twice as old as her daughter. Ten years ago, Sunita was three times as old as her daughter was then. Let the daughter's present age be x years and Sunita's be y years. What is Sunita's present age (in years)?
A36
B44
C40
D80
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Answer: C) 40
y = 2x and y - 10 = 3(x - 10). So 2x - 10 = 3x - 30, x = 20, y = 40 years.
5. Two pipes fill a tank. In an hour Pipe A delivers x litres and Pipe B delivers y litres. Together in one hour they deliver 90 litres, and Pipe A delivers 30 litres more than Pipe B. Using two linear equations, find how many litres Pipe A delivers in an hour.
A120
B54
C60
D66
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Answer: C) 60
x + y = 90 and x = y + 30. So (y + 30) + y = 90, 2y = 60, y = 30, x = 60 litres.