Solve the following problem from Mahavira Of a collection of

Solve the following problem from Mah¯av¯ira: “Of a collection of mango fruits, the king took 1 4 , the queen 1 3 of the remainder, and the three chief princes 1 4 , 1 3 , and 1 2 of the successive remainders, and the youngest child took the remaining three mangoes. O you who are clever in miscellaneous problems in fractions, give out the measure of that collection of mangoes.”

Solution

Let X = original number of mangoes

Remainder after king = 3x/4

Remainder after the queen = (2/3)*(3x/4)

Remainder after three cheif princes = (3/4)(2/3)(1/2)(2/3)(3x/4)

given that

(3/4)(2/3)(1/2)(2/3)(3x/4) = 3

solving this equation:

x/8 = 3

x = 24 mangoes