| Ram left \[\frac{1}{3}\] of his property to his widow and \[\frac{3}{5}\] of the remainder to his daughter. He gave the rest to his son who received Rs. 6400. How much was his original property worth? [SSC (10 + 2) 2014] |
A) Rs. 16000
B) Rs. 32000
C) Rs. 24000
D) Rs. 1600
Correct Answer: C
Solution :
| Let total property of Ram be Rs. x. |
| Then, share of his wife \[=\frac{x}{3}\] |
| and share of his daughter \[=\left( x-\frac{x}{3} \right)\times \frac{3}{5}\] |
| \[=\frac{2x}{3}\times \frac{3}{5}=\frac{2x}{5}\] |
| Now, share of his son \[=x-\frac{x}{3}-\frac{2x}{5}\] |
| \[=\frac{15x-5x-6x}{15}=\frac{4x}{15}\] |
| Now, share of son \[=\frac{4x}{15}\]\[\Rightarrow \]\[6400=\frac{4x}{15}\] |
| \[\Rightarrow \] \[4x=6400\times 15\] |
| \[\Rightarrow \] \[x=\frac{6400\times 15}{4}\] |
| \[\Rightarrow \] \[x=1600\times 15\] |
| \[\therefore \] \[x=Rs.\,24000\] |
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