NCERT Solutions Ganita Prakash Chapter 3 In-text Questions — Estimate the answer

Book page 70 & 71 Updated on2026-09-05

Q1.

Number of words in your maths textbook: a. More than 5000 b. Less than 5000

Answer

(a) More than 5000.

Words on one page ≈ 150
Number of pages ≈ 250
Total ≈ 150 × 250 = 37,500 words

Even if we count only 100 words on a page and 100 pages, we already get 10,000 — far more than 5,000. So the answer is clearly more than 5000.

Q2.

Number of students in your school who travel to school by bus: a. More than 200 b. Less than 200

Answer

For most schools the answer is (b) less than 200.

Students in the school ≈ 500
Children who come by bus ≈ one out of every four ≈ 500 ÷ 4 = 125

If your school runs 4 buses and each carries about 40 children, that is 4 × 40 = 160 — again less than 200.

Check it yourself: count the buses standing in your school and multiply by the seats in one bus. That is a good estimate, and it takes half a minute.

Q3.

Roshan wants to buy milk and 3 types of fruit to make fruit custard for 5 people. He estimates the cost to be ₹100. Do you agree with him? Why or why not?

Answer

No — ₹100 is a little too low. Let us estimate the shopping list for 5 people:

Item	Quantity	Approximate cost
Milk	1 litre	₹60
Bananas	4	₹25
Apple	2	₹50
Grapes / papaya	250 g	₹30
Sugar and custard powder	a small quantity	₹20
Total		about ₹185

So around ₹180 – ₹200 would be needed. Roshan could manage in ₹100 only if he uses half a litre of milk and buys the cheapest seasonal fruits (banana, papaya, guava) in small quantities.

The idea of estimation: we are not looking for the exact bill. We only want to know whether ₹100 is roughly right — and here it falls short by about half.

Q4.

Estimate the distance between Gandhinagar (in Gujarat) to Kohima (in Nagaland). Hint: Look at the map of India to locate these cities.

Answer

Gandhinagar is in the far west of India and Kohima is in the far east, so the two cities are almost as far apart as India is wide.

Width of India from west to east ≈ 3000 km
Straight-line distance Gandhinagar → Kohima ≈ 2400 km
Distance by road ≈ 3000 km

Answer: roughly 2,500 km in a straight line (about 3,000 km if you actually travel by road or rail).

Tip: use the scale printed on the map of India. Measure the gap between the two cities with a ruler and multiply by the scale.

Q5.

Sheetal is in Grade 6 and says she has spent around 13,000 hours in school till date. Do you agree with her? Why or why not?

Answer

No — 13,000 hours is far too high. Let us check with a quick calculation.

School hours in a day ≈ 6
School days in a year ≈ 220
Hours in one year = 6 × 220 = 1320 hours
Sheetal has studied for about 7 years (Class 1 to Class 6, plus one year of nursery)
Total ≈ 1320 × 7 = 9,240 hours

So about 9,000 – 10,000 hours is a sensible figure. To reach 13,000 hours she would have had to be in school for nearly 10 years, which is not possible in Class 6.

Why estimating helps: a big number can “feel” right but still be wrong. Breaking it into hours per day × days per year × number of years shows the truth in three steps.

Q6.

Earlier, people used to walk long distances as they had no other means of transport. Suppose you walk at your normal pace. Approximately, how long would it take you to go from: a. Your current location to one of your favourite places nearby. b. Your current location to any neighbouring state’s capital city. c. The southernmost point in India to the northernmost point in India.

Answer

A person walks about 5 km in one hour, and can comfortably walk about 25 km in a day (5 hours of walking).

Journey	Approximate distance	Time on foot
a. To a favourite place nearby (park, market, temple)	2 km	about 25 minutes
b. To a neighbouring state’s capital	about 500 km	about 20 days of walking
c. Kanniyakumari to the northern tip of India	about 3,200 km	about 128 days, i.e. more than 4 months

For (c): 3200 km ÷ 25 km a day = 128 days
Walking 8 hours a day at 5 km/h you would cover 40 km a day → 3200 ÷ 40 = 80 days

Did you know? This is exactly how pilgrims and traders travelled in ancient India — a journey from Kanniyakumari to Kashmir took several months.

Q7.

Make some estimation questions and challenge your classmates!

Answer

Here are estimation questions you can ask your friends. Remember, the fun is in explaining how you got your figure.

How many bricks were used to build our classroom wall?
How many chapatis does your family eat in one year?
How many words does your teacher speak during one period?
How many litres of water does your family use in a day?
How many buckets of water would fill the school’s overhead tank?
How many heartbeats have you had since you were born?
How many rupees does your family spend on vegetables in a month?

Sample answer — chapatis in a year:
5 people × 3 chapatis a meal × 2 meals a day = 30 a day
30 × 365 = about 11,000 chapatis a year

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