Question

gupta ate 1/6 of cookies.jeeva ate 1/5 of what was remaining.sheela ate 1/4 0f remaining. raga ate 1/3 what was left.lakshmi ate 1/2 of what was left.finally  there were 3 cookies left .how many cookies were totally made.

Answer 1

3 cookies were left in the end.
So, 3 is half of what was left after Raga ate.
So, No. of cookies left after Raga ate = 3 * 2
                                                            = 6

6 is $\frac{2}{3}$ of what was left after Sheela ate.
So,No. of cookies left after Sheela ate = 6 * $\frac{3}{2}$
                                                             = 9

9 is $\frac{3}{4}$ of what was left after Jeeva ate.
So, No. of cookies left after Jeeva ate = 9 * $\frac{4}{3}$
                                                             = 12

12 is $\frac{4}{5}$ of what was left after Gupta ate.
So, No. of cookies left after Gupta ate = 12 * $\frac{5}{4}$
                                                             = 15

15 is $\frac{5}{6}$ of the total.
So, Total no. of cookies = 15 * $\frac{6}{5}$
                                       = 18

There were 18 cookies in total.

Answer 2

let there are x cookies
gupta ate cookies=x/6
remaining cookies=x-x/6=5x/6
jeeva ate cookies=5x/30=x/6
remain cookies=5x/6 -x/6=4x/6=2x/3
sheela ate cookies=2x/3×1/4=2x/12=x/6
remain cookies=4x/6 -x/6=3x/6=x/2
ranga ate cookies=x/6
remain cookies=3x/6 - x/6=2x/6=x/3
laxmi ate=x/6
left cookies=2x/6 - x/6=x/6
According to question there are left 3 cookies
therefore
x/6=3⇒x=18
there was 18 cookies.there made 18 cookies