Question

Mohamed was given a large bag of sweets and ate one fifth of the sweets before stopping as he was feeling sick. the next day he ate one fourth of the remaining sweets and the following day he ate one fourth of the remainder, before counting the sweets he had left which totaled nine. how many sweets was he given in the beginning?

Answer 1

The total number of sweets given to Mohamed in the beginning is equals to 20.

As given in the question,

Let x be the total number sweets given to Mohamed in the beginning.

Number of sweets he ate when feeling sick = $\frac{x}{5}$  

Number of sweets left = x - (x /5)

                                   = (4x / 5)

Number of sweets he ate next day = $\frac{1}{4}$ × $\frac{4x}{5}$

                                                      = x /5

Number of sweets left  = (4x/5) - (x/5)

                                    = (3x /5)

Number of sweets he ate on the following day = $\frac{1}{4}$ ×$\frac{3x}{5}$

                                                                         = (3x / 20)

Number of sweets left at the end = (3x /5) - (3x/20)

                                                   = (12x-3x) / 20

                                                   = (9x /20)

As per given condition,

(9x / 20) = 9

⇒ x = (9 × 20)/9

⇒ x= 20

Therefore, the total number of sweets given to Mohamed in the beginning is equals to 20.

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