NCERT Solutions for Class 7th Maths Chapter 7 .1 Find the Unknowns — In-text Questions
Book page 165 – 1667 Updated on2026-09-19
Q1.
Find the unknown weight of the sack in the following cases.Fig. 7.9 — the weighing scale is balanced. [Hint: If we remove equal weights from both the plates, will the weighing scale still be balanced?]
Answer
The sack weighs 10 kg.
Left pan = sack + 2 kg Right pan = 10 kg + 2 kg = 12 kg
The scale is balanced, so
s + 2 = 12
s + 2 − 2 = 12 − 2 (take the 2 kg weight off both pans)
s = 10 kg
Why it happens: there is a 2 kg weight sitting on each pan. Lifting both off at the same moment removes the same amount from each side, so the scale stays balanced. What is left is one sack on the left and 10 kg on the right — and now the answer can simply be read off.
Tip: the aim in every one of these puzzles is to get the sacks alone on one pan. Every weight you can cancel off both pans brings you closer.
Q2.
Find the unknown weight of the sack in the following cases. In Fig. 7.10, all the sacks have the same weight.Fig. 7.10 — the weighing scale is balanced. All the sacks have the same weight. [Hint: Remove one sack from each plate for Fig. 7.10.]
Answer
Each sack weighs 14 kg.
Left pan = 2 sacks = 2s Right pan = 10 + 4 + one sack = 14 + s
The scale is balanced, so
2s = 14 + s
2s − s = 14 + s − s (remove one sack from each pan)
s = 14 kg
Removing one sack from each pan keeps the balance and leaves the answer in plain sight.
Why it happens: all the sacks weigh the same, so one sack on the left and one sack on the right are equal weights. Taking one off each pan removes the same amount from both sides, so the scale is still balanced. The right pan then holds only the fixed weights, 10 + 4 = 14 kg, and the left holds a single sack.
Check it yourself: two sacks weigh 28 kg. The other pan holds 10 + 4 + 14 = 28 kg. The scale balances. ✓
Q3.
Find the unknown weight of the sack in the following cases.Fig. 7.11 — the weighing scale is balanced. All the sacks have the same weight. [Hint: Can you remove objects so that the sacks are only on one plate?]
Answer
Each sack weighs 7 kg.
Left pan = 5 sacks = 5s
Right pan = 1 + 10 + 10 + 2 sacks = 21 + 2s
The scale is balanced, so
5s = 21 + 2s
5s − 2s = 21 + 2s − 2s (remove two sacks from each pan)
3s = 21
s = 21 ÷ 3 = 7 kg
Two sacks are common to both pans, so both can go.
Why it happens: the hint asks you to get the sacks onto one pan only. Two sacks appear on each side, so removing two from each side is removing the same weight from both — the balance survives. Three sacks are left facing 21 kg, and sharing 21 equally among 3 gives 7.
Check it yourself: five sacks weigh 5 × 7 = 35 kg. The right pan holds 21 + 7 + 7 = 35 kg. ✓
Q4.
Find the unknown weight of the sack in the following cases.Fig. 7.12 — the weighing scale is balanced. All the sacks have the same weight.
Answer
Each sack weighs 15 kg.
Left pan = 90 sacks + 50 kg = 90s + 50
Right pan = 60 sacks + 500 kg = 60s + 500
The scale is balanced, so
90s + 50 = 60s + 500
Remove 60 sacks from each pan:
30s + 50 = 500
Remove 50 kg from each pan:
30s = 500 − 50 = 450
s = 450 ÷ 30 = 15 kg
Why it happens: two removals are needed here, but each one is the same move as before. First the 60 sacks that sit on both pans go, leaving 30 sacks on the left. Then the 50 kg that the left pan carries is taken off both pans, leaving 30 sacks against 450 kg. Notice that we never had to know the weight of a sack to make either move — that is what makes the method powerful.
Check it yourself: 90 × 15 + 50 = 1350 + 50 = 1400 kg. And 60 × 15 + 500 = 900 + 500 = 1400 kg. The pans match. ✓