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NCERT Solutions Ganita Prakash (Part 1) Chapter 2 .5 Did You Ever Wonder? · A different way to say your age! — In-text Questions

Book page 392 Updated on2026-09-05

Q1.
“I’m ______ hours old!” said Roxie. Make an estimate before finding this number.
Answer

About 1,16,160 hours — roughly 1.2 × 105 hours.

Roxie said she is 4840 days old
1 day = 24 hours

Hours = 4840 × 24
= 4840 × 20 + 4840 × 4
= 96,800 + 19,360
= 1,16,160 hours ≈ 1.16 × 105

Estimate first: 4840 ≈ 5 × 103 and 24 ≈ 2.4 × 101, so the answer is about 12 × 104 = 1.2 × 105. The estimate is within 4% of the exact value.

Why it happens: the same age looks utterly different in different units — 13 years, 4840 days, 1.16 lakh hours. The quantity has not changed at all; only the size of the unit has. Choosing a smaller unit multiplies the number, and here the unit shrank by a factor of 24.
Q2.
“I am 69,70,710 … old”. What could this number mean? Find out!
Answer

It is Roxie's age in minutes.

Test the units one by one, starting from 4840 days.
In hours: 4840 × 24 = 1,16,160 — far too small
In minutes: 1,16,160 × 60 = 69,69,600 — matches!
In seconds: 69,69,600 × 60 = 41,81,76,000 — far too big

The book's 69,70,710 is 1110 minutes more than 69,69,600 — about 18½ hours, which is simply the part-day that has passed since she counted her 4840 days. So the answer is 69,70,710 minutes ≈ 7 × 106 minutes.

Why it happens: you can identify an unknown unit purely from the size of the number — its power of 10 is a fingerprint. 105 means hours, 107 means minutes, 108 would mean seconds. That is exactly the skill the whole "powers of 10" table on the following pages is training.
Q3.
Estu: “I am 4070 days old today. Can you find out my date of birth?”
Answer

Count backwards 4070 days from today.

4070 ÷ 365.25 = 11.14 years
= 11 years and about 0.14 × 365 ≈ 51 days

So Estu was born about 11 years and 7 weeks ago — which agrees with the book telling us he is 11 years old. To get the exact date, subtract in stages:

  1. Go back 11 years from today. That accounts for 11 × 365 + 3 leap days = 4018 days.
  2. 4070 – 4018 = 52 days still to go back. Subtract 52 more days from that date.

Worked out from 31 August 2026, this gives 10 July 2015. Do the same from your own "today" and you will get a date about 11 years and 7 weeks earlier.

Why it happens: years are not a whole number of days, so 365.25 (three ordinary years and one leap year) is the right average to divide by. Using 365 flat would put the answer out by about 11 days over 11 years — small, but enough to name the wrong date.
Q4.
If you have lived for a million seconds, how old would you be?
Answer

About 11½ days old — not even a fortnight.

1 day = 24 × 60 × 60 = 86,400 seconds ≈ 8.64 × 104 s

106 ÷ (8.64 × 104)
= (1 ÷ 8.64) × 106–4
= 0.1157 × 102
= 11.57 days (11 days and about 14 hours)
Why it happens: "a million" sounds like a large age, and it is a large number — but a second is a very small unit. Size in mathematics is always number × unit, and forgetting the unit is what makes such quantities feel wrong. For contrast, a billion seconds is 109 ÷ 8.64 × 104 ≈ 11,574 days ≈ 31.7 years, which really is an age.
Check it yourself: the jump from 106 to 109 seconds is a factor of 1000 — from a fortnight to a lifetime. That single comparison is the best illustration in the chapter of how fast powers of 10 climb.
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