# 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 3^{rd} 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.