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NCERT Solutions Ganita Prakash (Part 2) Chapter 1 In-text Questions — Percentage of Some Quantity

Book page 7 Updated on2026-09-05

Q1.
Try to calculate (without using pen and paper) the indicated percentages of the values shown in the table below. Write your answers in the table. [Columns: 100, 200, 50, 80, 10, 35, 287. Rows: 25% (100 → 25 is filled in), 10%, 20%, 5%.]
Answer
10020050801035287
25%255012.5202.58.7571.75
10%10205813.528.7
20%204010162757.4
5%5102.540.51.7514.35

None of these needs written work if you use the friendly fractions behind the percentages:

10% of a number = the number ÷ 10  (shift the decimal point one place left)
20% = double the 10% value
5% = half the 10% value
25% = one quarter, i.e. halve, then halve again

So for 287: 10% is 28.7 → 20% is 57.4 → 5% is 14.35 → 25% is 57.4 + 14.35 = 71.75.

Why it happens: 10% is 10/100 = 1/10, and dividing by 10 in a base-ten system is only a shift of the decimal point. Every other percentage in this table is built from that one easy step by doubling, halving or adding — which is why the table can be filled mentally.
Q2.
How did you find these values? Discuss the methods with the class. Do you find anything interesting in the table?
Answer

Several patterns run through the table:

  • The 20% row is exactly double the 10% row, in every column.
  • The 5% row is exactly half the 10% row.
  • 20% row + 5% row = 25% row, column by column (40 + 10 = 50, 16 + 4 = 20, 7 + 1.75 = 8.75, …).
  • Reading down any column, the values fall in the same order as the percentages — because the base is the same in that column.
(20/100 × y) + (5/100 × y) = (25/100 × y)
Why it happens: All four rows are the same number y multiplied by different hundredths. So the row values are proportional to the percentages themselves: doubling the percentage doubles the value, and adding two percentages adds their values. In algebra this is just the distributive law — (20/100)y + (5/100)y = (20 + 5)/100 × y.
Careful: This adding rule works only while the base y stays the same. 20% of one quantity plus 5% of a different quantity is not 25% of anything.
Q3.
Using this understanding, mentally calculate how much 40% of the values in the table above would be.
Answer

40% is double 20%, which is itself double 10%. So take a tenth and double it twice.

10020050801035287
10%10205813.528.7
40%40802032414114.8
40% of 287 → 10% is 28.7 → 20% is 57.4 → 40% is 114.8
Check it yourself: 40% is also 2/5. And 2/5 of 287 = 574/5 = 114.8. Same answer, different route.
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