NCERT Solutions Ganita Prakash (Part 1) Chapter 8 –194A Dramma-tic Donation — In-text Questions

Book page 193 Updated on2026-09-05

Q1.

“O wise one! A miser gave to a beggar ¹⁄₅ of ¹⁄₁₆ of ¹⁄₄ of ¹⁄₂ of ²⁄₃ of ³⁄₄ of a dramma. If you know the mathematics of fractions well, tell me O child, how many cowrie shells were given by the miser to the beggar.” (1 dramma = 1280 cowrie shells)

Answer

“Of” means multiply — so multiply all six fractions.

1/2 × 2/3 × 3/4 × 1/5 × 1/16 × 1/4
1/2 × 2/3 = 1/3
1/3 × 3/4 = 1/4
1/4 × 1/5 = 1/20
1/20 × 1/16 = 1/320
1/320 × 1/4 = 1/1280 of a dramma

1 dramma = 1280 cowrie shells
Gift = 1/1280 × 1280
= 1 cowrie shell

Did you know? Bhāskarāchārya wrapped a joke inside the arithmetic — after all that grand-sounding fraction talk, the miser parted with a single cowrie, the smallest coin there was.

Q2.

If we assume 1 gold dinar = 12 silver drammas, 1 silver dramma = 4 copper panas, 1 copper pana = 6 mashakas, and 1 pana = 30 cowrie shells, then 1 copper pana = ¹⁄₄₈ gold dinar. 1 cowrie shell = ____ copper panas. 1 cowrie shell = ____ gold dinar.

Answer

Work backwards along the chain of coins.

1 pana = 30 cowrie shells
So 1 cowrie shell = 1/30 copper pana

1 pana = 1/48 gold dinar
1 cowrie shell = 1/30 × 1/48
= 1/1440 gold dinar

1 gold dinar	=	Value
in drammas	12 × 1	12 drammas
in panas	12 × 4	48 panas
in cowrie shells	48 × 30	1440 cowries

Why it works: each “1 of the bigger coin = n of the smaller coin” becomes “1 of the smaller = ¹⁄_n of the bigger”. Chaining the fractions multiplies them.

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