The easiest way to solve such questions is to use ratio. The question also tests you on the concept of 'one item unchanged'.

First 'if' :


Jack sells 60, Jill sells 30 a day.

Ratio of the number Jack sells to Jill sells each day
= 60 : 30
= 2 : 1


This ratio doesn't change no since they sold for same number of days (until Jill finished selling)

So Ratio of the number that Jack would have sold altogether to the number Jill would have sold

= 60 : 30
= 2 : 1


Jack is left with 300 chickens.



Second 'if' :

Jack sells 30, Jill sells 60 a day.

Ratio of the number they sell each day
= 30 : 60
= 1 : 2

This ratio doesn't change since they sold for same number of days (until Jill finished selling)

So Ratio of the number that Jack would have sold altogether to the number Jill would have sold

= 30 : 60
= 1 : 2


Jack is left with 930 chickens.

Next, realise that one item is unchanged.

Jill sold all her chickens in both cases.

So we should make the units the same for both ratios for Jill. The lowest common multiple of 1 and 2 is just 2 so just multiply the first ratio by 2.


First if :

Jack : Jill
= 2 : 1
= 4 : 2


Second if :

Jack : Jill
= 1 : 2



Comparing the two ratios for Jack,

4 - 1 = 3

We see that Jack would have sold 3 more units in the second case than in the first vase.


930 - 300 = 630

He had 630 more chickens left in the second case, so this means that he sold 630 less in it (or in other words, 630 more in the first case)

So 630 = 3 units

1 unit = 630 ÷ 3 = 210


Number of chickens Jack had in his farm

= 1 unit + 930
= 210 + 930
= 1140

Or

4 units + 300

= 210 × 4 + 300
= 840 + 300
= 1140

Thank you for your detailed explanation.

Welcome