Question

The ratio of Mr. Anil's annual income to expenditure is \[5:4\]. For Mr. Aman the same figure is \[3:2\]. Also, \[4\% \] of Aman's monthly income is equal to \[7\% \] of Anil's monthly income. If Anil's monthly expenditure is 96,000 rupees.
I.Find Aman's annual income.
II.savings made by Mr. Anil and Mr. Aman.

Answer 1

Hint: Here in the question, we have to find the Aman’s annual income and savings made by Mr Anil's and Mr. Aman’s. To solve this, let’s take Anil’s money as \[x\] and Aman’s money as \[y\] then multiply the anil’s income and expenditure ratio with \[x\] and multiply the Aman’s income and expenditure ratio with \[y\] and given the condition \[4\% \] of Aman's monthly income is equal to \[7\% \] of Anil's monthly income then simplify by using a percentage calculation and basic arithmetic operation, we get the required solution.

Complete step by step solution:
Consider the given:
Since, the ratio of Mr. Anil's annual income to expenditure is \[5:4\]
Let’s take \[x\] be a any number, then
Anil’s monthly income\[ = 5x\] and his expenditure\[ = 4x\].
Similarly, given the ratio of Mr. Aman’s annual income to expenditure is \[3:2\]
Let’s take \[y\] be a any number, then
Aman’s monthly income \[ = 3y\] and his expenditure \[ = 2y\].
Given\[4\% \] of Aman's monthly income is equal to \[7\% \] of Anil's monthly income, then we have
\[ \Rightarrow \,\,\,4\% \times 3y = 7\% \times 5x\]
Rewrite the ratio in to the fraction, then
\[ \Rightarrow \,\,\,\dfrac{4}{{100}} \times 3y = \dfrac{7}{{100}} \times 5x\]
\[ \Rightarrow \,\,\,\dfrac{{12y}}{{100}} = \dfrac{{35x}}{{100}}\]
On simplification, we get
\[ \Rightarrow \,\,\,12y = 35x\]------(1)
Given, Anil's monthly expenditure is 96,000 rupees.
\[ \Rightarrow \,\,4x = 96,000\]
Divide both side by 4, then
\[ \Rightarrow \,\,x = \dfrac{{96,000}}{4}\]
\[ \Rightarrow \,\,x = 24,000\]
Substitute the \[x\] value in equation (1). To get the value of \[y\]
\[ \Rightarrow \,\,\,12y = 35\left( {24,000} \right)\]
\[ \Rightarrow \,\,\,12y = 840000\]
Divide both side by 12, then
\[ \Rightarrow \,\,\,y = \dfrac{{840000}}{{12}}\]
\[ \Rightarrow \,\,\,y = 70000\]
Now, Find
I.Aman's annual income.
\[ \Rightarrow \,\,3 \times 70000\]
\[ \Rightarrow \,\,2,10,000\]
Thus, Aman’s annual income is \[2,10,000\]

II.Savings made by Mr. Anil and Mr. Aman.
As we know savings is the difference between income and expenditure, then
Anil’s savings
\[ \Rightarrow \,\,5x - 4x\]
\[ \Rightarrow \,\,x\]
\[\therefore \,\,24,000\]
Aman’s savings
\[ \Rightarrow \,\,3y - 2y\]
\[ \Rightarrow \,\,y\]
\[\therefore \,\,70,000\]
Hence, it’s a required solution.

Note: Ratio problems are word problems that use ratios to relate or compare the different items in the question. Remember the main things to be aware about for ratio problems are to change the quantities to the same unit if necessary and further simplify by the proper arithmetic operations.