Algebra Ratio and Proportion (Class 6)

What this worksheet covers

This is an eighteen-question practice worksheet on algebra, ratio and proportion for Class 6, 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 algebra, ratio and proportion at Class 6 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 in the space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Algebra Ratio and Proportion (Class 6) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. If x = 7, the value of 3x − 5 is _______.

   • A16correct
   • B21
   • C26
   • D12
   Solution: Substitute x = 7.
   3x − 5 = 3 × 7 − 5 = 21 − 5 = 16.

2. 2. The cost of 7 identical books is ₹441. What is the cost of 11 such books?

   • A₹630
   • B₹714
   • C₹693correct
   • D₹770
   Solution: Cost of 1 book = 441 ÷ 7 = ₹63.
   Cost of 11 books = 11 × 63 = ₹693.

3. 3. Consider the following statements.(i) A ratio has no units.(ii) The ratio 2 : 3 is the same as the ratio 3 : 2.(iii) An equation stays true if the same number is added to both sides.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(i) and (iii) onlycorrect
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is true — a ratio compares two like quantities, so the units cancel. Statement (ii) is false; order matters, and 2 : 3 is not the same as 3 : 2. Statement (iii) is true; this is the balancing rule used to solve equations. Hence (i) and (iii).