Question

Mr. Arun earns Rs. $9,500$ per month and his wife earns Rs. $8,000$. Find the ratio of –
a)Mr. Arun’s income to his wife’s income
b)Wife’s income to total income.

Answer 1

Hint: Here, from the given data will frame the mathematical expression and then simplify using basic mathematical multiples and division. Be good in numbers for the accurate and efficient answer.

Complete step-by-step answer:
Given that - Mr. Arun earns Rs. $9,500$ per month
a)Mr. Arun’s wife earns Rs. $8,000$ per month
Ratio of Mr. Arun’s income to his wife’s income $ = \dfrac{{Arun'\operatorname{s} \;income}}{{Arun's\;{\text{wife's income}}}}$
Place value in the above equation –
Ratio of Mr. Arun’s income to his wife’s income $ = \dfrac{{9500}}{{8000}}$
Take common factors from both the denominator and the numerator. Therefore remove from both the numerator and denominator.
Ratio of Mr. Arun’s income to his wife’s income $ = \dfrac{{95}}{{80}}$
We can observe that in the above equation- both the terms are multiple of therefore remove it and simplify
Ratio of Mr. Arun’s income to his wife’s income $ = \dfrac{{19}}{{16}}$ is the required answer.

b)Ratio of Wife’s income to total income
Now, the total income $ = $ Arun’s income $ + $ his wife’s income
Place values in the above equation –
Total income $ = 9500 + 8000$
Simplify –
Total income $ = 17500$
Now, Ratio of wife’s income to total income $ = \dfrac{{{\text{wife's income}}}}{{total{\text{ income}}\;}}$
Place values in the above equation –
Ratio of wife’s income to total income $ = \dfrac{{8000}}{{17500\;}}$
Take common factors from both the denominator and the numerator. Therefore remove from both the numerator and denominator.
Ratio $ = \dfrac{{80}}{{175\;}}$
We can observe that in the above equation- both the terms are multiple of therefore remove it and simplify
Ratio $ = \dfrac{{16}}{{35\;}}$
Hence, the required answer - Ratio of wife’s income to total income$ = \dfrac{{16}}{{35\;}}$.


Note: Always convert the given word statement in the correct mathematical form and simplify using basic mathematical operations. Ratio is the comparison between two numbers without any units. Whereas, when two ratios are set equal to each other are called proportion. Four numbers a, b, c, and d are said to be in proportion. If $a:b = c:d$ whereas, four numbers are said to be in continued proportion if $a:b = b:c = c:d$. Always remember that ratios are unitless numbers.