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(D) Total time $= 36$ months.Let Aditya's time of contribution $= t_A$ and Manish's time $= t_M$.Since $t_A + t_M = 36$,we have $t_M = 36 - t_A$.The r

Vedclass · Accepted Answer

$22$

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(D) Total time $= 36$ months.Let Aditya's time of contribution $= t_A$ and Manish's time $= t_M$.Since $t_A + t_M = 36$,we have $t_M = 36 - t_A$.The ratio of their profit shares is equal to the ratio of their investments multiplied by time: $(300 	imes t_A) : (500 	imes t_M)$.Total profit $= Rs. 1020$.Aditya's share $= Rs. 495$,so Manish's share $= 1020 - 495 = Rs. 525$.The ratio of their profits $= 495 : 525 = 33 : 35$.Equating the ratios: $\frac{300 	imes t_A}{500 	imes (36 - t_A)} = \frac{33}{35}$.Simplifying: $\frac{3 	imes t_A}{5 	imes (36 - t_A)} = \frac{33}{35} \Rightarrow \frac{t_A}{36 - t_A} = \frac{33}{35} 	imes \frac{5}{3} = \frac{11}{7}$.$7 	imes t_A = 11 	imes (36 - t_A) \Rightarrow 7t_A = 396 - 11t_A$.$18t_A = 396 \Rightarrow t_A = 22$ months.

Aditya and Manish continued in a joint business for $36$ months. Aditya contributed $Rs. 300$ for a certain time and Manish invested $Rs. 500$ for the remaining time. If out of a total profit of $Rs. 1020$,Aditya gets $Rs. 495$,then for how long (in months) did Aditya keep his money?

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