There were some guavas at a fruit stall. In the morning, 1/6 of the guavas were sold. In the afternoon, another 30 guavas were sold. The total number of guavas sold was 5 less than 7/12 of the number of guavas the fruit stall had at first.

Question

There were some guavas at a fruit stall. In the morning, 1/6 of the guavas were sold. In the afternoon, another 30 guavas were sold. The total number of guavas sold was 5 less than 7/12 of the number of guavas the fruit stall had at first.

(a) How many guavas were there at first?
(b) What fraction of the guavas in the stall remained unsold in the afternoon?

Answer 1

(a) Let x = # of guavas at first

1/6x + 30 = 7/12x - 5
35 = 7/12x - 1/6x
35 = (7x - 2x)/12
420/5 = 5x/5
x = 84 guavas at first
(b) sold guavas : 1/6 (84) + 30 = 44
unsold guavas : 84 - 44 = 40
fraction of unsold guavas : 40/84 = 10/21