NCERT Solutions for Class 7th Maths Chapter 7 Solving Problems — In-text Questions

Book page 177 – 179 Updated on2026-09-19

Q1.

Example 10: Solve 28 (x + 4) + 300 = 1000.

Answer

x = 21. The book gives three routes; all three end at the same place.

Way 1 — remove the term, then the factor
28(x + 4) + 300 = 1000
28(x + 4) = 1000 − 300 = 700
x + 4 = 700 ÷ 28 = 25
x = 25 − 4 = 21

Way 2 — divide the whole equation by 4 first
28, 300 and 1000 are all divisible by 4, so divide both sides by 4:
7(x + 4) + 75 = 250
7(x + 4) = 250 − 75 = 175
7x + 28 = 175
7x = 147, so x = 147 ÷ 7 = 21

Way 3 — open the bracket first
28x + 112 + 300 = 1000
28x + 412 = 1000
28x = 1000 − 412 = 588
x = 588 ÷ 28 = 21

Check: 28(21 + 4) + 300 = 28 × 25 + 300 = 700 + 300 = 1000 ✓

Why it happens: every route uses only the balance rule, so every route must land on 21. Which one is quickest depends on the numbers. Way 1 is shortest here because 700 ÷ 28 is exact. Way 2 is handy when a common factor makes the numbers smaller. Way 3 always works but produces the biggest arithmetic.

Tip: look at the numbers before you start. Spotting that 700 ÷ 28 = 25 saves several lines.

Q2.

Example 11: Riyaz asked Akash to perform the following steps: 1. Think of a number. 2. Subtract 3 from the number. 3. Multiply the result by 4. 4. Add 8 to the product. 5. Reveal the final answer. The final answer revealed by Akash was 24. Using this, Riyaz correctly figured out the starting number that Akash had thought of. Find this number.

Answer

Akash thought of 7.

Let the starting number be x, and follow the steps in symbols.

Step	Expression
Think of a number	x
Subtract 3 from the number	x − 3
Multiply the result by 4	4(x − 3) = 4x − 12
Add 8 to the product	4x − 12 + 8 = 4x − 4

The final answer was 24, so
4x − 4 = 24
4(x − 1) = 24
x − 1 = 24 ÷ 4 = 6 (divide both sides by 4)
x = 6 + 1 = 7

Check: 7 → 7 − 3 = 4 → 4 × 4 = 16 → 16 + 8 = 24 ✓

Why it happens: Riyaz never sees the middle steps, but he does not need to. All four steps together do just one thing to the starting number: they turn x into 4x − 4. Knowing that single expression is enough to undo the whole trick.

Q3.

Try the steps using different numbers as the starting number. Do you see any relation between the starting number and final answer?

Answer

Yes — the final answer is always 4 less than 4 times the starting number.

Start x	x − 3	× 4	+ 8 (final answer)	4x − 4
1	−2	−8	0	4(1) − 4 = 0 ✓
5	2	8	16	4(5) − 4 = 16 ✓
7	4	16	24	4(7) − 4 = 24 ✓
10	7	28	36	4(10) − 4 = 36 ✓
12	9	36	44	4(12) − 4 = 44 ✓

Another way to say it: each time the starting number goes up by 1, the final answer goes up by 4.

Why it happens: the algebra shows it in one line — the four steps together give 4x − 12 + 8, which is 4x − 4. The "− 3" and the "+ 8" do not disappear; they combine into a single "− 4" after the multiplication by 4 has stretched the − 3 into − 12.

Q4.

Can you think of a simple rule that you can use to get the starting number from the final answer?

Answer

Add 4 to the final answer and divide by 4. In short: starting number = (final answer ÷ 4) + 1.

final answer = 4x − 4
4x = final answer + 4
x = (final answer + 4) ÷ 4

Since 4x − 4 = 4(x − 1), the same rule can be written as
x = (final answer ÷ 4) + 1

Final answer	÷ 4	+ 1	Starting number
24	6	6 + 1	7
36	9	9 + 1	10
0	0	0 + 1	1

Why it happens: the trick multiplies by 4 and then shifts by −4, so undoing it means shifting back by +4 and then dividing by 4. Doing the inverse operations in the reverse order is what unlocks any such trick.

Try This: invent your own. "Think of a number, add 5, double it, subtract 4" gives 2x + 6, so your rule to undo it is (answer − 6) ÷ 2.

Q5.

Example 12: Ramesh and Suresh have 60 marbles between them. Ramesh has 30 more marbles than Suresh. How many marbles does each boy have? Use this to find both the unknowns. [Hint: denote Suresh's marbles as y and Ramesh's as y + 30, giving y + (y + 30) = 60.]

Answer

Suresh has 15 marbles and Ramesh has 45 marbles.

Let Suresh have y marbles. Then Ramesh has y + 30.
Total is 60, so
y + (y + 30) = 60
2y + 30 = 60
2y = 60 − 30 = 30
y = 30 ÷ 2 = 15 (Suresh)

Ramesh = y + 30 = 15 + 30 = 45

Check: 15 + 45 = 60 marbles in all ✓ and 45 − 15 = 30 more for Ramesh ✓

Why it happens: writing x + y = 60 and x = y + 30 gives two unknowns, and so far we can only solve equations with one. The trick is to use the second fact at once: since Ramesh always has 30 more than Suresh, we can call his count y + 30 instead of x. Now only y is unknown, and one equation is enough.

Tip: think of it as the balance again. Set aside Ramesh's extra 30 marbles; the remaining 30 marbles split equally between the two boys, 15 each. Ramesh then takes his 30 back, giving 45.

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