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NCERT Solutions for Class 7th Maths Chapter 5 Summer and Winter at the Same Time — Math Talk

Book page 118 – 121 Updated on2026-09-19

Q1.
The tables below show data related to weather in two cities in different countries. The numbers given are in hours. Can you guess what the data might be related to?

City 1

JanFebMarAprMayJunJulAugSepOctNovDec
210257372441536564555465394310222186

City 2

JanFebMarAprMayJunJulAugSepOctNovDec
459384381327304276295318369409435468
The two tables printed on page 118. Every number is in hours.
Answer

The numbers are the monthly hours of daylight — the number of hours in the month for which the Sun is at least partly above the horizon.

How you could guess it. Divide each month's figure by the number of days in that month and see whether the answer is sensible.

City 1, June: 564 ÷ 30 = 18.8 hours per day
City 1, December: 186 ÷ 31 = 6.0 hours per day

City 2, June: 276 ÷ 30 = 9.2 hours per day
City 2, December: 468 ÷ 31 = 15.1 hours per day

Every answer lies between 0 and 24 hours a day — so the data can be about something that happens for part of each day. Rain or wind would not follow such a smooth yearly curve, but daylight would.

The clue that settles it: the two cities move in opposite directions. City 1 peaks in June and bottoms in December; City 2 does exactly the reverse. Only something tied to the Earth's tilt behaves like that — the two cities must be in opposite hemispheres.
Tip: notice that dividing the monthly total by the number of days is itself finding an average — the average daylight per day for that month. That is exactly how the clustered bar graph in the book was drawn.
Q2.
Does this give some idea of where these two cities are located?
Answer

Yes. The pattern tells us two things about their positions, before we are told any names.

  • Opposite hemispheres. City 1 has its longest days in June, so it is in the Northern Hemisphere. City 2 has its shortest days in June, so it is in the Southern Hemisphere.
  • Far from the Equator. City 1 swings from about 19 hours of daylight a day in June to about 6 hours in December — a change of some 13 hours. Such a huge swing only happens well away from the Equator. City 2 swings from about 9 to about 15 hours, a change of 6 hours, so it is away from the Equator too, but not as far as City 1.
In June, City 1 has daylight for about 18.8 ÷ 24 ≈ 3/4 of the whole day.
In December, only about 6 ÷ 24 = 1/4 of the day.

The book confirms it: City 1 is Helsinki, Finland and City 2 is Wellington, New Zealand.

Why the seasons flip: in June the Northern Hemisphere is tilted towards the Sun, so days there are long and it is summer. At the same moment the Southern Hemisphere is tilted away, so its days are short and it is winter. The Earth's tilt gives the two hemispheres opposite seasons at the same time.
Did you know? Very close to the poles the tilt is so extreme that in midsummer the Sun does not set at all — the Midnight Sun, as at Andøya in Norway.
Q3.
Is there anything more that you wish to explore?
Answer

An open question. Here are directions this data really opens up.

  • Where does India fit? India lies much closer to the Equator, so its day lengths vary far less — roughly 10½ to 13½ hours in Delhi. Collect sunrise and sunset times for your own town for one year and compare the swing with Helsinki's.
  • What happens exactly at the Equator? Day and night stay close to 12 hours each, all year.
  • What happens above the Arctic Circle? The Sun never sets in midsummer and never rises in midwinter — daylight of 24 hours a day, and of 0.
  • Do the two cities' yearly totals match? City 1: 210 + 257 + 372 + 441 + 536 + 564 + 555 + 465 + 394 + 310 + 222 + 186 = 4512 hours. City 2: 459 + 384 + 381 + 327 + 304 + 276 + 295 + 318 + 369 + 409 + 435 + 468 = 4425 hours. Both are close to half of 8760 hours in a year, as you would expect.
  • Does long daylight mean hot weather? Not always — collect temperature data for the same cities and see.
  • How does this affect people's lives? School timings, electricity use, farming, sports — all shift with daylight.
Why the yearly totals are so alike: every place on Earth gets roughly half a year of daylight in total. Being far from the Equator changes when you get it, not how much you get.
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