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This is one of our many quizzes on Proportions. Click on this to access more such competitive quizzes on Ratio and Proportions.

Proportions Quiz 2

mathematics

 Conclude the fraction, when any fraction bears the same ratio to $\dfrac{1}{{33}}$ as $\dfrac{{11}}{8}$ does to $\dfrac{5}{{44}}$:

 Assume the fraction as variable first and then write the equation as per the question to find the value of the variable.

Let the fraction to be found be $X$. So, $ \\ X:\dfrac{1}{{33}} = \dfrac{{11}}{8}:\dfrac{5}{{44}} \\ \Rightarrow \dfrac{5}{{44}} \times X = \dfrac{1}{{33}} \times \dfrac{{11}}{8} \\ \Rightarrow \dfrac{5}{{44}}.X = \dfrac{1}{{24}} \\ \Rightarrow X = \dfrac{{11}}{{30}} \\ $ Therefore, the assumed fraction is $\dfrac{{11}}{{30}}$.

 What is the antecedent of a ratio, when its consequent is 35, and this ratio is equal to $5:7$ ?

 Assume the antecedent as a variable first. Then write the proportional equation as per the question, and then find the antecedent variable.

Let the antecedent be $X$. So, the ratio will be $X:35$. $ \\ X:35 = 5:7 \\ \Rightarrow \dfrac{X}{{35}} = \dfrac{5}{7} \\ \Rightarrow 7X = 175 \\ \therefore X = \dfrac{{175}}{7} = 25 \\ $ Therefore, the required antecedent is 25.

 The ratio of ages between two brothers A and B is $3:2$ and the product of their ages is 216. After 3 years, what is the age of your younger brother?

 Assume their ages first with respect to the given age ratio. And then further write the equation as per the question to find the value of the $x$ first.

Let the age of A and B be $3x\,and\,2x$ respectively. $ \\ $ Now, as per the question, the product of their ages is $216$ $ \\ \because 3x \times 2x = 216 \\ \Rightarrow 6{x^2} = 216 \\ \Rightarrow {x^2} = 36 \\ \Rightarrow x = \sqrt {36}  = 6 \\ $ So, A’s age $ = 3x = 3 \times 6 = 18years$ $ \\ $ B’s age $ = 2x = 2 \times 6 = 12years$ $ \\ $ Therefore, B is the smaller brother. $ \\ $ After 3 years, B’s age is $12 + 3 = 15years$

 The proportion of ages of 3 friends is $2:3:5$ and their average age is 30 years. What is the age of the eldest friend?

 First conclude the total age of them with the help of average age. And then assume their ages with variables with respect to the proportion. And then write the equation as per the question to find the value of the variable.

Their total age $ = 3 \times 30 = 90years$. $ \\ $ Let the ages of 3 friends be $2x,3x\,and\,5x$. $ \because 2x + 3x + 5x = 90 \\ \Rightarrow 10x = 90 \\ \Rightarrow x = 9 \\ $ So, their ages are $2x,3x\,and\,5x = 18years,27years\,and\,45years$. $ \\ $ Therefore, the eldest friend is of 45years.

 The ratio of saving and expenditure of a lady is $5:16$. If her monthly income is $Rs.5040$ , then what is her monthly expenditure?

 First assume the saving and expenditure with respect to the given ratio of it. And then as per the question, find the value of the variable.

Let the savings and the expenditure be $Rs.5x\,and\,Rs.16x$ respectively. $ \\ $ As we know- $Saving + Expenditure = Income$ $ \\ \because 5x + 16x = 5040 \\ \Rightarrow 21x = 5040 \\ \Rightarrow x = 240 \\ $ Therefore, the monthly required expenditure is $Rs.16x = Rs.16 \times 240 = Rs.3840$