Question

A man left 25% of his money to his mother, 55% of his money to his daughter and the remaining rupees 9000 rupees to his brothers. How much money did he leave? Find the share of mother and daughter.

Answer 1

Hint: We denote the total amount of money left by the man as $T=x$. We express the amount left for his mother $M,$ the amount he left for his daughter $D$ in terms of $x$ using the given percentages. We are given the remaining amount $B=9000$ rupees are left for his brothers. So we have $T=M+D+B$. We solve the equation to find $x$ and then $M,D.$

Complete step-by-step answer:
The percentage in mathematics is a number or ratio expressed as a fraction of 100. We denote the percentage of $p$ as $p \% $ where ‘%’ is a symbol of percentage. If we say $p \% $ of $x$ that means if we divide $x$ into hundreds we can allocate $p$ in each of the hundred. We can calculate the allocation $y$ using the rule,
\[y=\dfrac{p}{100}\times x\]


Let us assume the total amount of money left by the man as $T=x$ rupees. We are given the question that he left 25% of the money to his mother. So the amount of money left by the man for his mother $M$ in rupees is 25% of total money $T=x$ . We have,
\[M=\dfrac{25}{100}\times T=\dfrac{25}{100}\times x=0.25x\]
We are further given in the question that he left 55% of his money to his daughter. So the amount of money left by the man for his mother $D$ in rupees is 55% of total money $T=x$. So we have
\[D=\dfrac{55}{100}\times T=\dfrac{55}{100}\times x=0.55x\]
We are also given in the question that he left the remaining 9000 rupees to his brothers. So the amount $B$ left for his brothers in rupees is
\[B=9000\]
The total amount of money left by the man sum of the amounts he left for his brother, daughter and sister. So we have,
\[\begin{align}
  & T=M+D+B \\
 & \Rightarrow x=0.25x+.55x+9000 \\
 & \Rightarrow x=0.8x+9000 \\
 & \Rightarrow .2x=9000 \\
 & \Rightarrow x=\dfrac{9000}{0.2}=45000 \\
\end{align}\]
So the man left a total 45000 rupees for his relatives. The share of his mother of the total amount in rupees is,
\[M=0.25x=0.25\times 45000=11250\]
The share of his daughter of the total amount in rupees is
\[D=0.55x=0.55\times 45000=24750\]

Note: We can also describe the parts of a total sum in diagrams as pie charts where the angle of the arc of the pie chart $\theta $ is related to percentage $p \%$ of the part as $\dfrac{\theta }{360}=\dfrac{p}{100}$. We also note that $x \% $ of $y$ and $y \% $ of $x$ are equal.