Rani has some chocolates with her. If she gives `(2)/(5)` of the chocolates to her brother and `(1)/(3)` of total chocolates to her sister, then she is left with 20 chocolates. Find the number of chocolates tht Rani had initially.

Options

A. 75
B. 60
C. 15
D. None of these

Answer

A

Explanation

Let the number of chocolates with Rani be x.
Number of chocolates given to her brother `=(2)/(5)x`
Number of chocolates given to her sister `=(1)/(3)x`
Number of chocolates left with her =20
`rArrx-(2x)/(5)-(x)/(3)=20rArr(15x-6x-5x)/(15)=20`
`(4x)/(15)=20rArr4x=20xx15`
`x=(20xx15)/(4)`
`rArrx=5xx15`
`rArrx=75`
`:.` The number of chocolates with Rani =75