| Abhav gave 30% of his money to Vijay. Vijay gave 2/3rd of what he received to his mother. Vijay's mother gave 5/8th of the money she received from Vijay, to the grocer. Vijay's mother is row left with Rs. 600. How much money did Abhay have initially? [SBI (PO) Pre 2015] |
A) Rs. 6200
B) Rs. 8000
C) Rs. 6000
D) Rs. 8200
E) Rs. 10200
Correct Answer: B
Solution :
| Let the money Abhay had initially be Rs. x. |
| Amount received by Vijay = 30% of \[x=Rs.\frac{3}{10}x\] |
| Amount received by Vijay's mother |
| \[=Rs.\frac{3}{10}\times \frac{2}{3}x=Rs.\frac{1}{5}x\] |
| Amount received by grocer\[=Rs.\frac{5}{8}\times \frac{1}{5}x=Rs.\frac{x}{8}\] |
| Amount Vijay's mother is left with |
| \[=\left( \frac{x}{5}-\frac{x}{8} \right)=\frac{8x-5x}{40}=Rs.\frac{3x}{40}\] |
| According to the question, |
| \[\frac{3x}{40}=600\]\[\Rightarrow \]\[x=\frac{600}{3}\times 40\] |
| \[\Rightarrow \] \[x=Rs.\,8000\] |
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