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NCERT Solutions for Class 7th Maths Chapter 4 In-text Questions — Look Before You Leap!

Book page 89 – 90 Updated on2026-09-19

Q1.
Do you know which month has this extra day?
Answer

February.

In an ordinary year February has 28 days. In a leap year it has 29, and the year has 366 days instead of 365.

Ordinary year: 365 days, February has 28 days
Leap year: 366 days, February has 29 days
Why it happens: the Earth takes 365.2422 days to go round the Sun, but a calendar can only count whole days. The leftover 0.2422 of a day is saved up, and after four years it has grown to about one whole day (4 × 0.2422 = 0.9688). That saved-up day is added to the shortest month.
Did you know? 29 February is called an intercalary day. Someone born on it gets a birthday only once every four years!
Q2.
What is the number of days that the Earth needs to make 4 full revolutions around the Sun?
Answer

1460.9688 days.

4 × 365.2422
3652422 × 4 = 14609688
Decimal places: 4 + 0 = 4
= 1460.9688 days

The calendar, meanwhile, counts

4 × 365 + 1 = 1461 days
Why it happens: the calendar with one leap day every four years gives 1461 days, but the Earth needs only 1460.9688. The calendar is ahead by 1461 − 1460.9688 = 0.0312 days every four years. Tiny — but it adds up, which is what the rest of the section is about.
Q3.
Math Talk: With this new scheme of adding one extra day every 4th year, what is the number of days in 100 calendar years? Can you write an expression to calculate that number?
Answer

36,525 days.

Each calendar year has 365 days → 100 × 365 = 36500 days
Years divisible by 4 get one extra day → 100/4 = 25 extra days

(100 × 365 + 100/4 × 1) = 36500 + 25 = 36,525 days
Why it happens: the expression counts in two layers. First give every year the basic 365 days. Then hand out one bonus day to each of the 25 leap years. Adding the bonus separately is easier than sorting the years into two groups first.
Q4.
How many years are divisible by 4 in 100 years?
Answer

25 years.

The multiples of 4 from 1 to 100 are 4, 8, 12, …, 100
Count = 100 ÷ 4 = 25
Why it happens: the multiples of 4 come one in every block of four consecutive years. A hundred years hold 25 such blocks, so there are 25 of them. Note that 100 itself is divisible by 4, so it is counted — this matters on the next page, where year 100 has to be taken out again.
Q5.
Math Talk: Can you form different expressions for the same question?
Answer

Yes. Here are three that all give 36,525.

1. Basic days plus bonus days:
(100 × 365) + (100/4 × 1) = 36500 + 25 = 36,525

2. Sort the years into two groups first:
(25 × 366) + (75 × 365) = 9150 + 27375 = 36,525

3. Pretend every year is a leap year, then take back the extra days:
(100 × 366) − 75 = 36600 − 75 = 36,525
Why it happens: all three count the same collection of days, only grouped differently. The first adds a bonus, the second splits the years into leap and ordinary, the third over-counts and then corrects. Being able to move between such expressions is what makes a calculation easy to check.
Compare: the Earth actually needs 100 × 365.2422 = 36,524.22 days for 100 revolutions. The calendar has 36,525 — it is ahead by 0.78 days. We have overcompensated.
Q6.
Math Talk: Can you write an expression for the number of days in 100 calendar years with this new adjustment? (no extra day in the 100th year)
Answer

36,524 days.

Years divisible by 4 in 100 years = 100/4 = 25
But 100 itself must be left out → subtract 100/100 = 1
Leap years = 100/4 − 100/100 = 25 − 1 = 24
Ordinary years = 100 − 24 = 76

(100/4 − 100/100) × 366 + (100 − (100/4 − 100/100)) × 365
= (24 × 366) + (76 × 365)
= 8784 + 27740
= 36,524 days
Why it happens: the old scheme gave 36,525 days against the Earth's 36,524.22 — too many by 0.78 of a day. Removing one leap day per century takes the calendar down to 36,524, which is now short by only 0.22 of a day. Much closer.
Q7.
This is close to 36524.22 days but is it close enough? What happens after 1000 years with this adjustment?
Answer

Over 1000 years the small shortfall grows to 2.2 days — so it is not close enough.

Calendar days in 1000 years = 36524 × 10 = 3,65,240 days
Days the Earth needs = 1000 × 365.2422 = 3,65,242.2 days

Difference = 365242.2 − 365240 = 2.2 days
Why it happens: a shortfall of 0.22 days per century is repeated ten times in a thousand years, and 10 × 0.22 = 2.2. Now the calendar is behind the Earth, the opposite of the earlier problem. To bridge the gap the calendar makers put one leap day back: every 400th year is a leap year after all.
Result: with that final rule, 1000 calendar years hold (750 × 365) + (240 × 366) + (8 × 365) + (2 × 366) = 3,65,242 days, against the Earth's 3,65,242.2 — just 0.2 days apart in a thousand years.
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