EN हिं

NCERT Solutions for Class 7th Maths Chapter 4 End-of-chapter question set — Figure it Out

Book page 93 – 95 Updated on2026-09-19

Q1.
A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper?
Answer

The potato chips are cheaper.

The packets are different sizes, so compare the price of the same weight of each — say 100 g.

Chikki: 70.5 ÷ 210 per gram
Price of 100 g = 70.5 × 100 ÷ 210 = 7050 ÷ 210 = ₹33.57 (nearly)

Chips: 33.25 ÷ 110 per gram
Price of 100 g = 33.25 × 100 ÷ 110 = 3325 ÷ 110 = ₹30.23 (nearly)

₹30.23 is less than ₹33.57, so 100 g of chips costs less than 100 g of chikki.

Why it happens: "cheaper" cannot be judged from the price on the packet alone, because ₹70.5 buys nearly twice as much weight as ₹33.25. Only a unit rate — price for one gram, or for 100 g — puts the two on the same footing.
Tip: a quick mental check. Two chips packets weigh 220 g and cost ₹66.50; that is more weight than the chikki packet (210 g) for less money than ₹70.5. So the chips must be cheaper per gram.
Q2.
Write the decimal number at the arrow mark: (first line marked 3.1 and 3.2, second line marked 2.15 and 2.17)
Answer

First line: 3.16. Second line: 2.162.

Each line is cut into 10 equal parts, and on both lines the arrow stands on the 6th mark after the left end.

Line 1: from 3.1 to 3.2 is 0.1
One part = 0.1 ÷ 10 = 0.01
Arrow = 3.1 + 6 × 0.01 = 3.1 + 0.06 = 3.16

Line 2: from 2.15 to 2.17 is 0.02
One part = 0.02 ÷ 10 = 0.002
Arrow = 2.15 + 6 × 0.002 = 2.15 + 0.012 = 2.162
3.16 3.1 3.2 2.162 2.15 2.17
Both lines have ten equal parts. The taller middle mark is the halfway point — 3.15 on the first line, 2.16 on the second — and the arrow sits one step to its right.
Why it happens: always read the two labelled ends first and count the gaps between them, not the marks. Ten gaps means each gap is one-tenth of the distance. On the second line that distance is only 0.02, so each gap is 0.002 — and the answer needs three decimal places, even though the labels show only two.
Tip: the taller mark in the middle is a helpful anchor. The arrow is one small step beyond 3.15, and one small step beyond 2.16.
Q3.
Shyamala bought 3 kg bananas at ₹30/- per kg. She counted 35 bananas in all. She sells each banana for ₹5/-. How much profit does she make selling all the bananas?
Answer

Her profit is ₹85.

Cost price = 3 × 30 = ₹90
Selling price = 35 × 5 = ₹175
Profit = 175 − 90 = ₹85
Why it happens: she buys by weight but sells by count, so the two amounts must be worked out separately before they can be compared. The 35 bananas are the same 3 kg — just measured a different way.
Tip: profit per banana = 175 ÷ 35 − 90 ÷ 35 = 5 − 2.571… ≈ ₹2.43. Multiplying that by 35 gives ₹85 again, but working with the totals is far cleaner here.
Q4.
A teacher placed textbooks that are 2.5 cm thick on a bookshelf. The teacher wanted to place 80 textbooks on the shelf. The bookshelf is 160 cm long. How many books could be placed on the shelf? Was there any space left? If yes, how much?
Answer

Only 64 books fit, and no space is left — the 64 books fill the shelf exactly.

Number of books = 160 ÷ 2.5
Clear the divisor: (160 × 10) ÷ (2.5 × 10) = 1600 ÷ 25
25 × 64 = 1600
= 64 books

Space used = 64 × 2.5 = 160 cm
Space left = 160 − 160 = 0 cm
Why it happens: the teacher wanted 80 books, but 80 × 2.5 = 200 cm — that is 40 cm more shelf than there is. So 16 books have to go elsewhere. Since 2.5 divides 160 exactly, the shelf is filled with nothing to spare.
Check it yourself: four books stand 10 cm wide, so 160 cm holds 16 groups of four — that is 64 books. ✓
Q5.
Fill in the following blanks appropriately: 5.5 km = ___ m; 35 cm = ___ m; 14.5 cm = ___ mm; 68 g = ___ kg; 9.02 m = ___ mm; 125.5 ml = ___ l
Answer

Going to a smaller unit multiplies, going to a bigger unit divides.

ConversionRelationMove the pointAnswer
5.5 km = ? m1 km = 1000 m× 1000, 3 places right5500 m
35 cm = ? m1 m = 100 cm÷ 100, 2 places left0.35 m
14.5 cm = ? mm1 cm = 10 mm× 10, 1 place right145 mm
68 g = ? kg1 kg = 1000 g÷ 1000, 3 places left0.068 kg
9.02 m = ? mm1 m = 1000 mm× 1000, 3 places right9020 mm
125.5 ml = ? l1 l = 1000 ml÷ 1000, 3 places left0.1255 l
Why it happens: the metric units are built on tens, so every conversion is a multiplication or division by 10, 100 or 1000 — and that is only the decimal point sliding. A smaller unit needs a bigger count, so the point moves right; a bigger unit needs a smaller count, so it moves left.
Tip: ask yourself first whether the answer should be bigger or smaller than the number you started with. 68 g is a small weight, so in kilograms it must be much less than 1 — 0.068, not 68000.
Q6.
The following problem was set by Sridharacharya in his book, Patiganita. “6 1/4 is divided by 2 1/2, and 60 1/4 is divided by 3 1/2. Tell the quotients separately.” Can you try to solve it by converting the fractions into decimals?
Answer

First quotient: 2.5. Second quotient: 17.2142857… (about 17.21).

Change the mixed numbers to decimals first.
6 1/4 = 6 + 0.25 = 6.25
2 1/2 = 2 + 0.5 = 2.5
60 1/4 = 60.25
3 1/2 = 3.5
First division: 6.25 ÷ 2.5
= (6.25 × 10) ÷ (2.5 × 10) = 62.5 ÷ 25
25 × 2 = 50, remainder 12.5 → 125 Tenths ÷ 25 = 5 Tenths
= 2.5

Second division: 60.25 ÷ 3.5
= (60.25 × 10) ÷ (3.5 × 10) = 602.5 ÷ 35
35 × 17 = 595, remainder 7.5
75 Tenths ÷ 35 → 2 Tenths, 5 Tenths remain
50 Hundredths ÷ 35 → 1, 15 remain … the digits 142857 begin to repeat
= 17.2142857… ≈ 17.21
Why it happens: as a fraction the second answer is 241/14, and 14 = 2 × 7. The 7 is not a factor of any power of ten, so the quotient cannot stop — and the repeating block turns out to be our old friend 142857 from page 85. The first answer, 25/10, has a denominator made only of 2s and 5s, so it ends after one place.
Did you know? Śrīdharācārya wrote the Pāṭīgaṇita in the 9th century CE. Decimal notation did not exist in his form then — he set the problem entirely in fractions, and we are simply reading it in a newer script.
Q7.
Math Talk: Fill the boxes in at least 2 different ways: (a) □ × □ = 2.4 (b) □ × □ = 14.5
Answer

Split the answer into two factors, then move the point between them.

(a) 2.4
1.2 × 2 = 2.4
0.8 × 3 = 2.4
0.6 × 4 = 2.4
12 × 0.2 = 2.4
2.4 × 1 = 2.4

(b) 14.5
2.9 × 5 = 14.5
1.45 × 10 = 14.5
5.8 × 2.5 = 14.5
29 × 0.5 = 14.5
0.29 × 50 = 14.5
Why it happens: start from a whole-number product. 2.4 is 24 tenths, and 24 = 12 × 2 = 8 × 3 = 6 × 4, so every factor pair of 24 gives an answer once one factor is divided by 10. Likewise 14.5 is 145 tenths, and 145 = 5 × 29 — so 5 and 29 are the only whole-number pieces to work with.
Tip: whatever you do to one factor, undo in the other. Halving 2.9 to 1.45 means doubling 5 to 10, and the product stays 14.5.
Q8.
Find the following quotients given that 756 ÷ 36 = 21: (a) 75.6 ÷ 3.6 (b) 7.56 ÷ 0.36 (c) 756 ÷ 0.36 (d) 75.6 ÷ 360 (e) 7560 ÷ 3.6 (f) 7.56 ÷ 0.36
Answer

Compare each division with 756 ÷ 36 and see how far the two points have moved.

DivisionRewrite as whole numbersQuotient
(a)75.6 ÷ 3.6756 ÷ 3621
(b)7.56 ÷ 0.36756 ÷ 3621
(c)756 ÷ 0.3675600 ÷ 362100
(d)75.6 ÷ 360756 ÷ 36000.21
(e)7560 ÷ 3.675600 ÷ 362100
(f)7.56 ÷ 0.36756 ÷ 3621
Why it happens: multiplying both the dividend and the divisor by the same number leaves the quotient alone. In (a) both were divided by 10, in (b) both by 100 — so both still give 21. In (c) only the divisor shrank (by 100), so the quotient grew 100 times. In (d) only the divisor grew (by 100 compared with 3.6), so the quotient shrank.
Note: parts (b) and (f) are the same division printed twice, so they have the same answer, 21.
Q9.
Find the missing cells if each cell represents a÷b: columns a = 1517, 151.7, 15.17, 1.517, 15170; rows b = 37, 3.7, 0.37, 0.037, 370. (Given: 1517 ÷ 37 = 41; 15.17 ÷ 3.7 = 4.1; 151.7 ÷ 0.037 = 4100)
Answer

Every cell holds the digits 41 — only the point moves.

b ↓   a →1517151.715.171.51715170
37414.10.410.041410
3.7410414.10.414100
0.374100410414.141000
0.03741000410041041410000
3704.10.410.0410.004141
Why it happens: the digits of a are always 1517 and the digits of b are always 37, and 1517 ÷ 37 = 41. So every cell is 41 with the point shifted. Moving right along a row divides a by 10, so the quotient is divided by 10. Moving down a column divides b by 10, so the quotient is multiplied by 10. Notice the diagonal of 41s: those are the cells where a and b have been shifted by the same amount, which cancels out.
Check it yourself: 0.041 × 37 = 1.517. ✓ And 410000 × 0.037 = 15170. ✓
Q10.
Using the digits 2, 4, 5, 8, and 0 fill the boxes □□.□ × □.□ to get the: (a) maximum product (b) minimum product (c) product greater than 150 (d) product nearest to 100 (e) product nearest to 5
Answer

There are 120 ways to place the five digits. Here are the best ones.

ArrangementProduct
(a) maximum54.0 × 8.2442.80
(b) minimum45.8 × 0.29.16
(c) greater than 15084.5 × 2.0169.00
(d) nearest to 10020.5 × 4.898.40
(e) nearest to 545.8 × 0.29.16
Why it happens:
  • Maximum: the two leading digits matter most, so the biggest digits 8 and 5 should sit in the tens place of one factor and the ones place of the other. The 0 is then dumped in a tenths place where it costs least. 82.0 × 5.4 also gives 442.80.
  • Minimum: put the 0 in the ones place of the short factor, making it 0.2 — the smallest factor possible. Then 45.8 × 0.2 = 9.16. No arrangement can go below this, so (b) and (e) share the same answer.
  • Greater than 150: half of the 120 arrangements (50 of them) clear 150, so there are many correct answers. 84.5 × 2.0 = 169 is an easy one.
  • Nearest to 100: 20.5 × 4.8 = 98.40 is 1.6 away. The next best, 40.8 × 2.5 = 102.00, is 2 away.
Tip: estimate before you multiply. 54 × 8 ≈ 432 and 82 × 5 ≈ 410 tells you at once that the answer to (a) is near 440.
Q11.
Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c) 245.05 ÷ 7.9682 (d) 245.05 ÷ 0.942368 (e) 245.05 (f) 7.9682
Answer

Increasing order: (f) < (c) < (a) < (e) < (d) < (b)

You can sort them without doing a single long multiplication. Compare each multiplier and divisor with 1.

ExpressionReasoningValue
(f)7.9682a small number on its own7.9682
(c)245.05 ÷ 7.9682divided by a number > 1, so much smaller than 245.05≈ 30.75
(a)245.05 × 0.942368multiplied by a number just under 1, so a little less than 245.05≈ 230.93
(e)245.05the number itself245.05
(d)245.05 ÷ 0.942368divided by a number just under 1, so a little more than 245.05≈ 260.04
(b)245.05 × 7.9682multiplied by a number > 1, so much bigger≈ 1952.61
Why it happens: 245.05 is the anchor. Multiplying by 0.942368 (just below 1) pulls it slightly down; dividing by it pushes slightly up. Multiplying by 7.9682 (well above 1) pushes it far up; dividing by it pulls it far down. So (a) and (d) sit close on either side of (e), while (c) and (b) sit far away on either side. Finally 7.9682 by itself is smaller than every one of them.
Check it yourself: 245.05 × 7.9682 = 1952.607410 exactly, and 245.05 × 0.942368 = 230.92727840 exactly. The two divisions do not end, so they are given to two decimal places.
Was this helpful?