# Proportionately II

Last week we discussed how we can perform the division (16400 ÷ 25) mentally just by doubling both the dividend and divisor twice to get (65600 ÷ 100) and then disregarding the zeroes in the end to arrive at the quotient 656.

This is because a division problem can be considered as a direct proportion between the dividend and the divisor with the quotient as the constant of proportionality.  We will now consider another problem which was given in the 3rd International Vedic Mathematics Olympiad, Lower Primary level which can be easily solved largely by halving.

“At a fruit farm, lemons are placed in trays each holding 24. Four trays make up one box. How many boxes are needed for 21120 lemons?

A 216

B 218

C 220

D 222

E 224”

We can find first how many trays of lemons are there:

(21120 ÷ 24)/2 = 10560 ÷ 12

(10560 ÷ 12)/2 = 5280 ÷ 6

(5280 ÷ 6)/2 = 2640 ÷ 3

(2640 ÷ 3)/3 = 880 trays

Now since there are 4 trays in a box, we need to divide 880 by 4. This is easily done also by halving.

(880 ÷ 4) = 440 ÷ 2

(440 ÷ 2)/2 = 220 ÷ 1

220 boxes are needed for the 21120 lemons.