Question

An old man has an amount of Rs. 15,00,000 in hand. He gave $\dfrac{1}{3}rd$ of it to his son, $\dfrac{3}{5}th$ of it to his daughter, $\dfrac{1}{20}th$ to his servant and the rest to the charity. How much did he give to charity?

Answer 1

Hint: The total amount of money with the old man is Rs. 15,00,000. So, we will first find out the amount of money he gave to his son, daughter and servant by using the fraction formula, that is the amount of money received by his son, which will be = $\dfrac{1}{3}\times $ total amount. Similarly, we will find the money received by his daughter and servant. Then we will find the sum of the amount of money received by his son, daughter and servant and subtract it from the total amount of money to get the money that he gave to charity.

Complete step-by-step answer:
We have been given that the old man has an amount of Rs. 15,00,000. We have also been given that he gave $\dfrac{1}{3}rd$ of it to his son, $\dfrac{3}{5}th$ of it to his daughter, $\dfrac{1}{20}th$ to his servant and the rest to the charity. And we have to find the money he gave to the charity. So, first we will find out howm money he gave to his son, daughter and servant.
We have been given that he gave $\dfrac{1}{3}rd$ of the total money to his son, which means his son receives,
$\dfrac{1}{3}\times total\text{ }money$
$\begin{align}
  & \Rightarrow \dfrac{1}{3}\times 15,00,000 \\
 & \Rightarrow Rs.5,00,000\ldots \ldots \ldots \left( i \right) \\
\end{align}$
Now, we have also been given that he gave $\dfrac{3}{5}th$ of the money to his daughter, so she receives,
$\begin{align}
  & \Rightarrow \dfrac{3}{5}\times 15,00,000 \\
 & \Rightarrow Rs.9,00,000\ldots \ldots \ldots \left( ii \right) \\
\end{align}$
And he gave $\dfrac{1}{20}th$ to his servant, so the servant receives,
$\begin{align}
  & \Rightarrow \dfrac{1}{20}\times 15,00,000 \\
 & \Rightarrow Rs.75,000\ldots \ldots \ldots \left( iii \right) \\
\end{align}$
So, we can say that the,
Total money = Money received by son + daughter + servant + charity.
So, we can say,
Money, he gave to charity = Total money - money received by son - daughter - servant.
So, using the values from equations (i), (ii) and (iii), we get,
Money to charity = 15,00,000 - 5,00,000 - 9,00,000 - 75,000 = 15,00,000 - 14,75,000 = Rs. 25,000.
Hence, he gave Rs. 25,000 to the charity.

Note: We can solve this question in an alternate method also. The total money he gave to his son, daughter and servant can be calculated as,
 $\begin{align}
  & =\dfrac{1}{3}\times total\text{ }money+\dfrac{3}{5}\times total\text{ }money+\dfrac{1}{20}\times total\text{ }money \\
 & \Rightarrow \left( \dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{20} \right)\times total\text{ }money \\
\end{align}$
By taking the LCM, we will get,
$\begin{align}
  & \left( \dfrac{20+36+3}{60} \right)\times total\text{ }money \\
 & \Rightarrow \dfrac{59}{60}\times total\text{ }money \\
\end{align}$
We know that the total money = Rs. 15,00,000. So, we get,
$\begin{align}
  & \dfrac{59}{60}\times 15,00,000 \\
 & \Rightarrow Rs.14,75,000 \\
\end{align}$
So, this means that the old man gave Rs. 14,75,000 to his son, daughter and servant. So, the money he gave to charity will be,
Total money - Rs. 14,75,000 , which is, Rs. 15,00,000 - Rs. 14,75,000 = Rs. 25,000.
So, we get that he gave Rs. 25,000 to charity.