NCERT Solutions Ganita Prakash (Part 2) Chapter 1 –4Section 1.1 Fractions as Percentages — Figure it Out

Book page 3 Updated on2026-09-05

Q1.

Express the following fractions as percentages. (i) 3/5 (ii) 7/14 (iii) 9/20 (iv) 72/150 (v) 1/3 (vi) 5/11

Answer

A fraction is of one unit and a percentage is per 100 units, so multiply each fraction by 100.

(i) 3/5 × 100 = 300/5 = 60%
(ii) 7/14 = 1/2, and 1/2 × 100 = 50%
(iii) 9/20 × 100 = 900/20 = 45%
(iv) 72/150 = 12/25, and 12/25 × 100 = 1200/25 = 48%
(v) 1/3 × 100 = 100/3 = 33.33% (exactly 33⅓%)
(vi) 5/11 × 100 = 500/11 = 45.45% (45.4545… %)

Why it happens: Writing 3/5 as a percentage means finding the equivalent fraction with 100 in the denominator: 3/5 = 60/100. Multiplying by 100 does exactly that in one step, because (3/5) × 100 is the numerator that sits over 100.

Check it yourself: (v) and (vi) do not stop. 1/3 and 5/11 have denominators with prime factors other than 2 and 5, so no equivalent fraction of theirs can have denominator 100 — their percentages are non-terminating decimals, and we round.

Q2.

Nandini has 25 marbles, of which 15 are white. What percentage of her marbles are white? (i) 10% (ii) 15% (iii) 25% (iv) 60% (v) 40% (vi) None of these

Answer

(iv) 60%.

White marbles as a fraction of all marbles = 15/25
15/25 = 15 × 4 / 25 × 4 = 60/100
= 60%

Why it happens: Option (ii) 15% is the trap. 15 is the count of white marbles, not the percentage — it would only be 15% if the total were 100. The whole here is 25, so each marble is worth 4% of the collection, and 15 marbles are worth 15 × 4 = 60%.

Q3.

In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?

Answer

Fraction who walk = 15/80 = 3/16
Percentage = 3/16 × 100 = 300/16
= 18.75%

Tip: A quick estimate first: 15 out of 80 is a little less than 20 out of 80, and 20 out of 80 is exactly a quarter, i.e. 25%. So the answer must be a bit under 25% — 18.75% fits.

Q4.

A group of friends is participating in a long-distance run. The positions of each of them after 15 minutes are shown in the following picture. Match (among the given options) what percentage of the race each of them has approximately completed. [Runners A, B, C, D are marked between Start and Finish; the options are 55%, 20%, 38%, 72%, 84%, 93%.]

Answer

Reading each runner's position as a fraction of the whole Start-to-Finish line:

Runner	Position on the line	Matching option
A	a little over a third of the way	38%
B	just past the halfway mark	55%
C	about three-quarters of the way	72%
D	almost at the Finish	93%

The four runners placed on the Start-to-Finish line, with the option each one matches.

The options 20% and 84% are not used — no runner is that close to the Start, and none sits between C and D.

Why it happens: The whole race is the whole line, so “percentage completed” is just the runner's distance from Start divided by the total length, times 100. Because the options are far apart, you can match them by eye: halfway is 50%, quarter-way is 25%, and so on.

Q5.

Pairs of quantities are shown below. Identify and write appropriate symbols ‘>’, ‘<’, ‘=’ in the blanks. Try to do it without calculations. (i) 50% ____ 5% (ii) 5/10 ____ 50% (iii) 3/11 _____ 61% (iv) 30% ____ 1/3

Answer

(i) 50% > 5% — 50 hundredths against 5 hundredths
(ii) 5/10 = 50% — 5/10 = 50/100
(iii) 3/11 < 61% — 3/11 is under 3/10, i.e. under 30%
(iv) 30% < 1/3 — 1/3 = 33⅓%

Why it happens: None of these needs long division. (iii): 3/11 is smaller than 3/10 because a bigger denominator cuts the whole into smaller pieces, and 3/10 is only 30% — far below 61%. (iv): a third of 100 is 33⅓, and 30 is less than that. Comparing sizes is often faster than computing values.

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