Direct and Inverse Proportions (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on direct and inverse proportions for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on direct and inverse proportions at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done on the blank space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Direct and Inverse Proportions (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. If x and y are in direct proportion, then _______ stays constant.

   • A{x/y}correct
   • Bx × y
   • Cx + y
   • Dx − y
   Solution: In direct proportion the two quantities increase and decrease together in the same ratio, so {x/y} = k, a constant. Equivalently, y = kx.

2. 2. 15 workers can build a wall in 48 hours. How long would 20 workers of the same ability take?

   • A36 hourscorrect
   • B30 hours
   • C40 hours
   • D64 hours
   Solution: Workers and time are in inverse proportion, so worker-hours stay constant:
   15 × 48 = 20 × t
   720 = 20t, so t = 36 hours.

3. 3. 6 pipes can fill a tank in 1 hour 20 minutes. How long will 5 such pipes take to fill it?

   • A1 hour 36 minutescorrect
   • B1 hour 30 minutes
   • C1 hour 40 minutes
   • D2 hours
   Solution: Pipes and time are in inverse proportion. First convert to minutes: 1 hour 20 minutes = 80 minutes.
   6 × 80 = 5 × t
   480 = 5t, so t = 96 minutes = 1 hour 36 minutes.