NCERT Solutions for Class 7th Maths Chapter 2 In-text Questions — A Quick Recap of Integers

Book page 25 Updated on2026-09-19

Q1.

Rakesh gives you a challenge. “I have thought of two numbers”, he says. “Their sum is 25, and their difference is 11.” Can you tell me the two numbers?

Answer

The two numbers are 18 and 7.

Work down the table the way the book does. Keep the sum fixed at 25 and watch how the difference changes.

First number	Second number	Sum	Difference
10	15	25	–5
20	5	25	15
19	6	25	13
18	7	25	11

18 + 7 = 25 ✓
18 – 7 = 11 ✓

Why it happens: every time you move 1 unit from the second number to the first, the sum stays 25 but the difference goes up by 2. From (20, 5) the difference is 15; move one step to (19, 6) and it drops to 13; one more step to (18, 7) and it is 11. So the difference marches in steps of 2, and you only have to walk it to the number you want.

Tip: you can also jump straight there. The bigger number is half of (sum + difference) and the smaller is half of (sum – difference).

First = (25 + 11) ÷ 2 = 36 ÷ 2 = 18
Second = (25 – 11) ÷ 2 = 14 ÷ 2 = 7

Q2.

“Think of two numbers whose sum is 25, but their difference is –11.” Use the same method. Try different pairs of numbers and fill in the table again.

First Number	Second Number	Sum	Difference

The same guess-table as on page 24 — first number, second number, their sum and their difference — ready to be filled in again.

Answer

The numbers are 7 and 18 — the same pair as before, but swapped.

First number	Second number	Sum	Difference
15	10	25	5
10	15	25	–5
8	17	25	–9
7	18	25	–11

7 + 18 = 25 ✓
7 – 18 = –11 ✓

Why it happens: the difference means first number – second number. Swapping the two numbers leaves the sum untouched, but it flips the difference to its additive inverse. So a puzzle with difference –11 is the difference-11 puzzle read backwards.

Check it yourself: the shortcut works here too. First = (25 + (–11)) ÷ 2 = 14 ÷ 2 = 7, and Second = (25 – (–11)) ÷ 2 = 36 ÷ 2 = 18.

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