The banker's discount on Rs. 2400 at 12 % p.a | vedclass

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(B) Let the time be $T$ years and the rate be $R = 12 \%$.Banker's Discount $(BD)$ on $Rs. 2400$ is given by $BD = \frac{P 	imes R 	imes T}{100} = \

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$5$

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(B) Let the time be $T$ years and the rate be $R = 12 \%$.Banker's Discount $(BD)$ on $Rs. 2400$ is given by $BD = \frac{P 	imes R 	imes T}{100} = \frac{2400 	imes 12 	imes T}{100} = 288T$.True Discount $(TD)$ on $Rs. 2520$ is given by $TD = \frac{Amount 	imes R 	imes T}{100 + (R 	imes T)} = \frac{2520 	imes 12 	imes T}{100 + 12T}$.Given that $BD = TD$,we have $288T = \frac{2520 	imes 12 	imes T}{100 + 12T}$.Since $T 
eq 0$,we can divide by $T$: $288 = \frac{30240}{100 + 12T}$.$288(100 + 12T) = 30240$.$28800 + 3456T = 30240$.$3456T = 30240 - 28800 = 1440$.$T = \frac{1440}{3456} = \frac{5}{12}$ years.Time in months $= \frac{5}{12} 	imes 12 = 5$ months.

The banker's discount on $Rs. 2400$ at $12 \%$ p.a. is the same as the true discount on $Rs. 2520$ for the same time and at the same rate. The time is (in months):

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