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NCERT Solutions Ganita Prakash (Part 1) Chapter 2 –342.5 Did You Ever Wonder? — In-text Questions

Book page 33 Updated on2026-09-05

Q1.
What would be the worth (in rupees) of the donated jaggery? What would be the worth (in rupees) of the donated wheat?
Answer

First write down the relationships, then put numbers into them.

Worth of jaggery (₹) = Roxie's weight in kg × cost of 1 kg jaggery
Worth of wheat (₹) = Estu's weight in kg × cost of 1 kg wheat

Nothing can be computed until the four unknowns are estimated. Reasonable assumptions for a 13-year-old and an 11-year-old, at present prices:

Roxie ≈ 45 kg, jaggery ≈ ₹70 per kg
Worth of jaggery = 45 × 70 = ₹3150

Estu ≈ 50 kg, wheat ≈ ₹50 per kg
Worth of wheat = 50 × 50 = ₹2500
Why it happens: the mathematics here is one multiplication; the real work is modelling — deciding which quantities matter and how they are related. Once the relationship is written down, missing values can be estimated and the answer follows. Your figures may differ from these and still be perfectly correct, so long as the assumptions are sensible and stated.
Q2.
Make necessary and reasonable assumptions for the unknowns and find the answers. Remember, Roxie is 13 years old and Estu is 11 years old.
Answer

State each assumption, then compute. Here is one complete set.

UnknownAssumptionReason
Roxie's weight (13 yrs)45 kgtypical for that age
Estu's weight (11 yrs)50 kgthe book's own figure
Jaggery₹70 / kglocal market rate
Wheat₹50 / kglocal market rate
Jaggery: 45 × 70 = ₹3150
Wheat: 50 × 50 = ₹2500
Together ≈ ₹5650, that is about ₹5.7 × 103
Why it happens: the answer is only as good as the assumptions, so give the result to the accuracy the assumptions deserve — "about ₹5000–6000" is honest, "₹5650.00" pretends to a precision nobody has. This is the same idea as the coefficient in scientific notation: how many digits you write should reflect how well you know the number.
Q3.
Roxie wonders, “Instead of jaggery if we use 1-rupee coins, how many coins are needed to equal my weight?”. How can we find out?
Answer

Relate the quantities first:

Number of coins = Roxie's weight ÷ weight of one 1-rupee coin

Roxie's weight is known (≈ 45 kg). The weight of one coin is not — so measure it. A single coin is too light for a kitchen balance, so weigh 100 coins together and divide by 100. That gives about 4 g per coin.

45 kg = 45,000 g
Number of coins ≈ 45,000 ÷ 4
= 11,250 coins ≈ 1.1 × 104
Why it happens: weighing 100 coins instead of one is a real measuring technique, not a trick. Any error in reading the balance is spread over 100 coins, so the error in the per-coin figure is 100 times smaller. Whenever a single item is too small to measure, measure many and divide.
Q4.
Would the number of coins be in hundreds, thousands, lakhs, crores, or even more? Make an instinctive guess.
Answer

In thousands — around ten thousand.

A coin weighs a few grams, so roughly 250 coins make 1 kg
250 × 45 ≈ 11,000 coins
Order of magnitude: about 104

Lakhs would need each coin to weigh less than half a gram — lighter than a small paper clip. Hundreds would need each coin to weigh over 100 g, heavier than a mobile phone. Both are clearly wrong, and you can rule them out before doing any arithmetic.

Why it happens: a good guess is not a wild one. Fix the two extremes by asking what the answer would force the coin to weigh, discard the impossible ones, and you are usually left with the right power of 10. Getting the exponent right is most of the battle; the coefficient can wait.
Q5.
Find the answer by making necessary and reasonable assumptions and approximations for the unknowns. Remember, we are not looking for an exact answer but a reasonably close estimate.
Answer
Assume: Roxie's weight = 45 kg = 45,000 g
Assume: one 1-rupee coin = 4 g

Number of coins = 45,000 ÷ 4 = 11,250
≈ 1.1 × 104 coins, worth ₹11,250

How sensitive is this? If the coin actually weighs 3.5 g the answer is about 12,900; if it weighs 5 g it is 9,000. Every reasonable assumption lands between 9,000 and 13,000 — so the answer is "about ten thousand coins", and that is as much as the data can support.

Why it happens: testing how the answer moves when an assumption is changed is the way to tell how far to trust it. Here the answer never leaves the 104 range, so the order of magnitude is solid even though the exact figure is not. That distinction — solid exponent, soft coefficient — is the practical heart of this section.
Q6.
Estu asks, “What if we use 5-rupee coins or 10-rupee notes instead? How much money could it be?” Make an instinctive guess first. Then find out (make necessary and reasonable assumptions about the unknown details and find the answers).
Answer

Guess: the 5-rupee coins should be worth more than the 1-rupee coins, and the notes far more than either — a note weighs almost nothing.

ItemAssumed weightNumber in 45 kgValue
1-rupee coin4 g11,250₹11,250
5-rupee coin6 g7,500₹37,500
10-rupee note1 g45,000₹4,50,000
5-rupee coins: 45,000 g ÷ 6 g = 7,500 coins × ₹5 = ₹37,500
10-rupee notes: 45,000 g ÷ 1 g = 45,000 notes × ₹10 = ₹4,50,000
Why it happens: the value of a weight of money is (value per piece) ÷ (weight per piece), multiplied by the total weight. Notes win overwhelmingly because that ratio is enormous for paper — ₹10 per gram against ₹1 per 4 grams. Roughly, notes give 40 times as much money per kilogram as 1-rupee coins.
Try This: repeat with ₹500 notes. The same 45 kg becomes about ₹2.25 crore — a jump of 50 times, purely because of the number printed on the paper.
Q7.
Estu says, “When I become an adult, I would like to donate notebooks worth my weight every year”. Roxie says, “When I grow up, I would like to do annadāna (offering grains or meals) worth my weight every year”. How many people might benefit from each of these offerings in a year? Again, guess first before finding out.
Answer

Take adult weights of about 60 kg each.

Notebooks. One notebook of 100 pages ≈ 200 g
60 kg = 60,000 g → 60,000 ÷ 200 = 300 notebooks
If each student receives 5 notebooks:
300 ÷ 5 = 60 students a year
Annadāna. One meal uses about 150 g of grain
60,000 ÷ 150 = 400 meals
= 400 people once, or about 1 person every day for a year, or 100 families of 4
Why it happens: both answers turn on "how much does one unit weigh", and the two units are wildly different in mass — a notebook is worth more than a meal in weight, so fewer notebooks are donated but each helps a student for months. Notice also that these are yearly gifts: over a 40-year working life the notebooks alone reach about 2400 students.
Did you know? Tulābhāra, offering goods equal to one's own weight, is a very old practice and is still followed in many places in Southern India. It is a token of gratitude and it supports the community.
Q8.
Roxie and Estu overheard someone saying — “We did pādayātra for about 400 km to reach this place! We arrived early this morning.” How long ago would they have started their journey?
Answer

About 12 to 13 days ago — roughly two weeks.

Assume a comfortable walking speed = 4 km per hour
Assume 8 hours of walking a day (with rests and nights off)

Distance covered per day = 4 × 8 = 32 km
Days needed = 400 ÷ 32 = 12.5 days

Test the assumptions. At 3 km/h for 6 h a day it is 400 ÷ 18 ≈ 22 days; at 5 km/h for 10 h a day it is 400 ÷ 50 = 8 days. So the honest answer is "somewhere between one and three weeks, most likely about a fortnight".

Why it happens: a pādayātra is not a race, so the daily distance — not the speed — is the quantity that really controls the answer. Once you fix a plausible 30 km or so a day, the arithmetic is a single division. Guessing before calculating is worth doing here: most people's first guess is far too short, because we judge distance by how long a bus takes.
Did you know? Pādayātra is the traditional practice of walking long distances as part of a religious or spiritual pursuit. Ajmer Sharif Dargah Ziyarat, Pandharpur Wari, Kānwar Yatra, Sabarimala Yatra, Sammed Shikharji Yatra and the Lumbini to Sarnath Yatra are some well-known examples.
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