Question

A woman has a certain number of mangoes of which 13% are bad. She gives 75% of the remainder as free to children charity and then finally she has 261 left. How many mangoes did she have initially?

Answer 1

Answer:1200 mangoes

Step-by-step explanation:

let initially she had x mangoes

bad mangoes =13% of x

good mangoes=(100-13)% of x=87% of x

mangoes given as charity=75% of 87% of x

mangoes left with the woman=(100-75)% of 87% of x=261

                                                 =25% of 87% of x=261

                                                 =x=(261*100*100)/(87*25)

                                                     =1200          

Answer 2

A women has a certain number of mangoes. Let the number be x

Among them, 13% of them are bad.

Number of good ones

$= x - 13 \% \: \sf \: of \: x \: \\ \\ = x - \frac{13}{100} x \\ \\ = \frac{100 - 13}{100} x \\ \\ = \frac{87}{100} x$

Now out of these mangoes She donates 75% as charity.

Number of mangoes donated

$=75 \% \sf \: of \: ( \frac{87x}{100} ) \\ \\ = \frac{3}{4} \times \frac{87}{100} x \\ \\ = \frac{261}{400} x$

Number of mangoes left with her

$=25 \% \sf \: of \: ( \frac{87x}{100} ) \\ \\ = \frac{1}{4} \times \frac{87}{100} x \\ \\ = \frac{87}{400} x$

But from the question it is given, She has 261 left.

So,

$\frac{87}{400} \times x = 261 \\ \\ x = \frac{261}{87} \times 400 \\ \\ x= 3 \times 400 \\ \\ x = 1200$

Therefore, she had 1200 mangoes initially.