NCERT Solutions Ganita Prakash (Part 1) Chapter 1 –21.1 A Lakh Varieties! — In-text Questions

Book page 1 Updated on2026-09-05

Q1.

Estu wondered, “One lakh! So far I have only tasted 3 varieties. If we tried a new variety each day, would we even come close to tasting all the varieties in a lifetime of 100 years?” What do you think? Guess.

Answer

No — not even close. One new variety a day for 100 years gives only about 36,500 varieties, which is roughly a third of a lakh.

Days in 1 year = 365 (ignoring leap years)
Days in 100 years = 365 × 100 = 36,500
Varieties tasted = 36,500 × 1 = 36,500
Still needed = 1,00,000 − 36,500 = 63,500 varieties

Why it happens: A lakh is 1,00,000. A whole 100-year lifetime has only about 36,500 days, so even one variety every single day from birth to death covers barely 36% of a lakh. That is how big a lakh really is.

Tip: Even with leap days (about 25 extra days per century) the total is only about 36,525 — still nowhere near a lakh.

Q2.

But how much is one lakh? Observe the pattern and fill in the boxes given below. (The largest 3-digit number is 999 → the smallest 4-digit number is ___ → the largest 4-digit number is ___ → the smallest 5-digit number is ___ → the largest 5-digit number is ___ → the smallest 6-digit number is 1,00,000; and the chain 99,995 → 99,996 → ___ → 99,998 → ___ → … )

Answer

Each arrow is simply “+ 1”, so every largest number is one step below the next smallest number.

Statement	Number
The largest 3-digit number is	999
The smallest 4-digit number is	1,000
The largest 4-digit number is	9,999
The smallest 5-digit number is	10,000
The largest 5-digit number is	99,999
The smallest 6-digit number is	1,00,000

The chain of ten boxes below it is just counting on by 1:

99,995 → 99,996 → 99,997 → 99,998 → 99,999 → 1,00,000 → 1,00,001 → 1,00,002 → 1,00,003 → 1,00,004

Why it happens: 99,999 is the largest number you can write with 5 digits. Adding 1 makes every 9 roll over to 0 and pushes a fresh 1 into a brand-new place — the lakhs place. That is exactly how 1,00,000, read as “one lakh”, is born.

Q3.

What if a person ate 3 varieties of rice every day? Will they be able to taste all the lakh varieties in a 100 year lifetime? Find out.

Answer

Yes — with 3 varieties a day a person just crosses one lakh.

Days in 100 years = 365 × 100 = 36,500
Varieties in 100 years = 36,500 × 3
= 36,500 × 3 = 1,09,500
1,09,500 > 1,00,000, extra = 9,500 varieties

Why it happens: With 2 varieties a day you get 36,500 × 2 = 73,000, which falls 27,000 short. The jump from 2 to 3 adds another 36,500 and that is what pushes the total past a lakh.

Check it yourself: How many varieties a day are needed to reach a lakh in just 50 years? Days = 18,250, so you would need 1,00,000 ÷ 18,250 ≈ 5.5, that is at least 6 varieties every day.

Was this helpful? Report an error