NCERT Solutions for Class 7th Maths Chapter 4 In-text Questions — how calendars were worked out (2026-27)

Q1.

Do you wonder how people figured out that the Earth completes one revolution around the Sun in exactly 364.2422 days?

Answer

By watching the sky patiently for a very long time and then dividing.

The method is simple to describe, though it needs great care.

Fix a moment that repeats every year — for example the day the shadow of a pole at noon is longest (the winter solstice), or the day the Sun rises exactly due east (an equinox).
Count the whole days from one such moment to the same moment many years later.
Divide the total number of days by the number of years.

If 100 years are found to hold 36,524.22 days, then
one year = 36524.22 ÷ 100 = 365.2422 days

Why it happens: one year alone cannot be measured to four decimal places — no one can note the exact instant of a solstice that finely. But spreading the error over a hundred years divides it by a hundred as well. That is why the number is written with four decimal places only after long records are collected.

Note: the book prints 364.2422 here, but on pages 88, 89, 91 and 92 the figure used is 365.2422 days. The correct value is 365.2422; 364.2422 is a printing slip.

Q2.

Try This: Investigate how traditional calendars in India managed to consistently align the days in the calendar with astronomical events like the Earth going around the Sun or even the positions of the stars in the sky accurately.

Answer

Indian calendars are luni-solar: the months follow the Moon, while the year is kept in step with the Sun.

What to look for in your investigation:

A lunar month (new Moon to new Moon) is about 29.53 days, so twelve of them make about 354.37 days — roughly 11 days short of a solar year.
Left alone, the festivals would slide backwards through the seasons, as they do in a purely lunar calendar.
The Indian solution is an extra month, the adhika māsa (also called Purushottama māsa), inserted about every 3 years — 7 extra months in 19 years.

19 solar years = 19 × 365.2422 ≈ 6939.6 days
235 lunar months = 235 × 29.5306 ≈ 6939.7 days
And 235 = (19 × 12) + 7 — the seven extra months

Sample answer: "The Sūrya Siddhānta and later the Pañcāṅga tradition track the Sun's position through the twelve rāśis and the Moon's position through the 27 nakṣatras. A month in which no saṅkrānti (the Sun's entry into a new rāśi) occurs is declared an adhika māsa. Because the rule depends on the Sun's actual position and not on counting alone, the calendar corrects itself and festivals such as Makara Saṅkrānti stay tied to the same part of the year."

Why it works: the Gregorian calendar keeps a whole number of days by adding a leap day; the Indian calendar keeps a whole number of lunar months by adding a leap month. Both are the same idea — save up the leftover, then pay it back in one lump.

Tip: compare a Pañcāṅga with an ordinary calendar for one year and mark the tithis. Ask at home which festivals shift by about 11 days each year, and which ones do not.