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Class 7 Maths: Finding the Unknown, 8 practice questions with answers

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These are 8 practice questions on Chapter 7, Finding the Unknown, of the new NCERT Class 7 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover framing an equation from a pattern, two rules that give the same result, solving equations with the unknown on both sides, with a fraction and with brackets, two word problems, and mending a mistake in a solution. Every answer is checked by putting it back into the equation. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was checked by a test script and none of the chapter's own examples is reused, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 7, Part 2, Chapter 7, printed pages 164 to 190):

Framing equations

Question 1. Diyas are placed around a growing rangoli design: design number n uses 5n + 2 diyas. (a) How many diyas do designs 1, 2 and 3 use? (b) Which design uses exactly 92 diyas? (c) Can any design use exactly 100 diyas?

Answer: (a) 7, 12 and 17; (b) design 18; (c) no. (a) Put n = 1, 2 and 3 into 5n + 2: 7, 12 and 17. (b) Solve 5n + 2 = 92. Take 2 from both sides: 5n = 90. Divide both sides by 5: n = 18. Check: 5 × 18 + 2 = 92. (c) 5n + 2 = 100 gives 5n = 98, but 98 is not a multiple of 5, so n would not be a whole number: no design uses exactly 100 diyas. (Equations from patterns, pages 166 and 167; tile patterns, pages 174 and 175.)

Question 2. Rohan and Meera start from the same number. Rohan multiplies it by 3 and then adds 5. Meera just adds 17 to it. They end up with the same result. What was the number, and what result did they both get?

Answer: the number is 6, and both get 23. Call the number x. Rohan gets 3x + 5 and Meera gets x + 17, so 3x + 5 = x + 17. Take x from both sides: 2x + 5 = 17. Take 5 from both sides: 2x = 12. Divide by 2: x = 6. Check: Rohan 3 × 6 + 5 = 23 and Meera 6 + 17 = 23. (Unknown terms on both sides, Example 6, pages 171 and 172.)

Solving equations

Question 3. Solve 7x − 9 = 4x + 15 and check your answer.

Answer: x = 8. Take 4x from both sides: 3x − 9 = 15. Add 9 to both sides: 3x = 24. Divide by 3: x = 8. Check: left side 7 × 8 − 9 = 47 and right side 4 × 8 + 15 = 47, so the two sides are equal. (Solving equations systematically, pages 169 to 172.)

Question 4. Solve x/6 + 4 = 11.

Answer: x = 42. Take 4 from both sides: x/6 = 7. The 6 divides x, so removing it multiplies the other side by 6: x = 7 × 6 = 42. Check: 42 ÷ 6 + 4 = 7 + 4 = 11. (When one side is a quotient, page 173.)

Question 5. Solve 3(2y − 5) = 4(y + 1) − 7.

Answer: y = 6. Open the brackets: 6y − 15 = 4y + 4 − 7, that is, 6y − 15 = 4y − 3. Take 4y from both sides: 2y − 15 = −3. Add 15 to both sides: 2y = 12. Divide by 2: y = 6. Check: left side 3 × (12 − 5) = 21 and right side 4 × 7 − 7 = 21. (Equations with brackets, page 177.)

Word problems and mistakes

Question 6. A hall costs ₹1100 to book, plus ₹45 for each guest. A family has ₹4700 to spend. How many guests can come if they spend it all? Write and solve an equation.

Answer: 80 guests. Let g be the number of guests. The cost is 1100 + 45g, so 1100 + 45g = 4700. Take 1100 from both sides: 45g = 3600. Divide by 45: g = 80. Check: 1100 + 45 × 80 = 1100 + 3600 = 4700. (A fixed charge plus a charge per person, pages 175 and 176.)

Question 7. A mother is 26 years older than her son. Their ages add up to 58. How old is each?

Answer: the son is 16 and the mother is 42. Let the son's age be s, so the mother's is s + 26. Then s + (s + 26) = 58, so 2s + 26 = 58, 2s = 32 and s = 16. The mother is 16 + 26 = 42. Check: 16 + 42 = 58, and 42 − 16 = 26. (Two unknowns written with one letter, page 179.)

Question 8. A student solves 6x − 5 = 2x + 11 like this: "6x + 2x = 11 − 5, so 8x = 6." Find the mistake, solve it correctly, and check with Brahmagupta's formula x = (D − B) ÷ (A − C).

Answer: x = 4. The student moved 2x to the left without changing its sign, and moved −5 to the right without changing its sign. Taking 2x from both sides gives 4x − 5 = 11, and adding 5 to both sides gives 4x = 16, so x = 4. Check: 6 × 4 − 5 = 19 and 2 × 4 + 11 = 19. In the form Ax + B = Cx + D, A = 6, B = −5, C = 2 and D = 11, so the formula gives (11 − (−5)) ÷ (6 − 2) = 16 ÷ 4 = 4. (Mind the mistake, page 181; Brahmagupta's formula, page 184.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 163 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every answer was checked by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheets: Finding the Unknown, Class 7 worksheet and Simple equations, Class 7 to 9 worksheet. Printable, in English, Hindi and Marathi, with an answer key.