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# Srimati Lal won a lottery of Rs.2500000. One-fifth of the amount was donated to public health service, ${{\dfrac{2}{5}}^{th}}$ of the left was denoted to school and ${{\dfrac{3}{4}}^{th}}$ of the left to the army fund. How much money was donated to the army fund?

Last updated date: 13th Jun 2024
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Hint: In this question, we need to find the money donated to the army fund if the total amount was Rs.2500000 and a fraction of the amount was given to public health service, school, and army fund. First, we will calculate the money donated to the public health service by taking ${{\dfrac{1}{5}}^{th}}$ of the total amount. Then we will find the remaining money by subtracting money given to public health services from the total amount. Then we will find ${{\dfrac{2}{5}}^{th}}$ of the remaining money which becomes money donated to the school. Then again we will find the remaining money. At last, we will find ${{\dfrac{3}{4}}^{th}}$ of the remaining money which will be the money donated to the army fund. We will use: $\dfrac{x}{y}$ of z is given by $\dfrac{x}{y}\times z$.

Complete step-by-step solution
Here we are given total money as Rs.2500000.
We know that one-fifth of the amount was donated to public health services. So ${{\dfrac{1}{5}}^{th}}$ of Rs.2500000 becomes equal to $\dfrac{1}{5}\times 2500000=Rs.500000$.
Hence, the money given to public health service was Rs.500000.
Since ${{\dfrac{2}{5}}^{th}}$ of the left was donated to the school. So let us find the remaining money first.
Remaining money after donation to public health service = total money - money donated to public health service
$\Rightarrow Rs.2500000-Rs.500000=Rs.2000000$.
Hence money left after donation to public health service is Rs.2000000. Now, ${{\dfrac{2}{5}}^{th}}$ of this amount is donated to the school. So,
$\dfrac{2}{5}\times 2000000=Rs.800000$
Hence, Rs.800000 were donated to the school.
Money left after donation to school = money left after donation to public health service - money donated to the school.
$\Rightarrow Rs.2000000-Rs.800000=Rs.1200000$.
Hence, money left after donation to school was Rs.1200000.
Since, ${{\dfrac{3}{4}}^{th}}$ of the money was donated to the army fund so,
Money donated to the army fund $\dfrac{3}{4}\times 1200000=900000$.
Hence, money donated to the army fund is Rs.900000
Hence, option D is the correct answer.

Note: Students should note that fraction for the next donation is given for the remaining money after the last donation. Students can make the mistake of directly calculating ${{\dfrac{3}{4}}^{th}}$ of the total money as a final answer. While calculating the remaining money after donation to the school, make sure to subtract money donated to the school from the remaining money after donation to publish health services. Take care while calculating such large numbers