Extra Questions for Class 7 Maths Chapter 15: Finding the Unknown

Fresh practice questions for Class 7 Maths Chapter 15 “Finding the Unknown”, reinforcing equation-solving and word problems. These Class 7 Mathematics Chapter 15 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Q1. Solve: 5(x – 3) = 2x + 6

Answer: 5x-15=2x+6 ⇒ 3x=21 ⇒ x = 7. Check: 5(7-3)=20; 2(7)+6=20 ✓

Q2. Assertion-Reason — Assertion (A): The equation x + 7 = x + 2 has no solution. Reason (R): Subtracting x…

Assertion (A): The equation x + 7 = x + 2 has no solution.
Reason (R): Subtracting x from both sides gives 7 = 2, which is always false.

Answer: Both A and R are true, and R correctly explains A.

Q3. A number decreased by 15 is equal to twice the number decreased by 40. Find the number.

Answer: x-15=2x-40 ⇒ 25=x ⇒ x = 25. Check: 25-15=10; 2(25)-40=10 ✓

Q4. Spot the Error — A student solves 3x + 4 = 19 as: "3x = 19 + 4 = 23, so x = 23/3." What went wrong?

A student solves 3x + 4 = 19 as: “3x = 19 + 4 = 23, so x = 23/3.” What went wrong?

Answer: The student added 4 instead of subtracting it when moving it to the other side. Correct working: 3x = 19 – 4 = 15 ⇒ x = 5. Check: 3(5)+4=19 ✓

Q5. The sum of three consecutive integers is 72. Find the integers.

Answer: Let the integers be x, x+1, x+2. x+(x+1)+(x+2)=72 ⇒ 3x+3=72 ⇒ 3x=69 ⇒ x=23. The integers are 23, 24, 25. Check: 23+24+25=72 ✓

Q6. HOTS — A father's age is 4 times his son's age. In 5 years, the father will be 3 times as old…

A father’s age is 4 times his son’s age. In 5 years, the father will be 3 times as old as his son will be then. Find their present ages.

Answer: Let son’s age = x, father’s age = 4x. In 5 years: 4x+5 = 3(x+5) ⇒ 4x+5=3x+15 ⇒ x=10. Son = 10 years, father = 4(10) = 40 years. Check: in 5 years, son=15, father=45=3×15 ✓

Q7. Write an equation for: "7 less than 3 times a number is 20," then solve it.

Answer: 3x – 7 = 20 ⇒ 3x = 27 ⇒ x = 9. Check: 3(9)-7=20 ✓

Q8. Two numbers differ by 8. Twice the smaller number equals the larger number plus 5. Find both numbers.

Answer: Let the smaller = x, larger = x+8. 2x = (x+8)+5 ⇒ 2x=x+13 ⇒ x=13. Smaller = 13, larger = 21. Check: 2(13)=26; 21+5=26 ✓

Q9. Solve: (2x – 1)/3 = 5

Answer: 2x-1=15 ⇒ 2x=16 ⇒ x = 8. Check: (16-1)/3 = 5 ✓

Q10. Explain, in your own reasoning, why doing the same operation to both sides of an equation always keeps it balanced (referring back to the balance-scale idea from the start of the chapter).

Answer: An equation is like a balanced scale — both sides represent the same total value. If you add, subtract, multiply, or divide both sides by the same amount, both sides change by the same proportion, so they remain equal to each other — the balance is preserved. This is why solving an equation always involves performing identical operations on both sides until the unknown is isolated.

See also: NCERT Solutions for Class 7 Maths Chapter 15

Quick revision: Revision Notes for Class 7 Maths Chapter 15

Frequently Asked Questions

How would you solve the equation 3x plus 7 equals 22 for the value of x?
Subtracting 7 from both sides gives 3x equals 15, and then dividing both sides by 3 gives x equals 5, isolating the unknown variable by reversing the operations applied to it.

Why is it important to perform inverse operations in the correct reverse order when solving a multi-step equation?
Since an equation is built up by applying operations to a variable in a certain sequence, solving it requires undoing those operations in the opposite order to maintain the balance of the equation.

Written by Satish

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