Question : The tax on the salary of C is $\frac{1}{4}$th of the salary and savings are $\frac{1}{3}$rd of the salary. The ratio of the expenditures to the savings is_____.
Option 1: 4 : 5
Option 2: 4 : 3
Option 3: 5 : 4
Option 4: 3 : 4
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Correct Answer: 5 : 4
Solution : Let the salary of C be $12a$. ⇒ Tax $= 12a × \frac14 = 3a$ And, savings $= 12a × \frac13=4a$ ⇒ Expenditure $= 12a - 3a - 4a=5a$ ⇒ Ratio of expenditure : saving $= 5a : 4a=5 : 4$ Hence, the correct answer is 5 : 4.
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Question : Choose the option in which the numbers are in the correct ascending order.
Option 1: $\frac{4}{5}, \frac{2}{3}, \frac{1}{11}$ and $\frac{2}{9}$
Option 2: $\frac{1}{11}, \frac{2}{9}, \frac{2}{3}$ and $\frac{4}{5}$
Option 3: $\frac{2}{9}, \frac{1}{11}, \frac{4}{5}$ and $\frac{2}{3}$
Option 4: $\frac{2}{3}, \frac{4}{5}, \frac{1}{11}$ and $\frac{2}{9}$
Question : Alloy A contains metals x and y only in the ratio 5 : 2, while alloy B contains them in the ratio 3 : 4. Alloy C is prepared by mixing alloys A and B in the ratio 4 : 5. The percentage of $x$ in alloy C is:
Option 1: $55 \frac{1}{9}\%$
Option 2: $55 \frac{2}{9}\%$
Option 3: $55 \frac{5}{9}\%$
Option 4: $55 \frac{4}{9}\%$
Question : If $abc = 5$, what is the value of $(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+5 c^{-1}}+\frac{1}{1+\frac{c}{5}+a^{-1}})$?
Option 1: $5$
Option 2: $1$
Option 3: $\frac{1}{5}$
Option 4: $(a+b+c)$
Question : What is the value of $\left(\frac{1}{a} - \frac{1}{b} - \frac{1}{c}\right)$, if $\frac{2a - 5}{a} - \frac{4b - 5}{b} + \frac{6c + 5}{c} = 0$?
Option 1: $\frac{4}{5}$
Option 2: $-\frac{8}{5}$
Option 3: $\frac{2}{5}$
Option 4: $-\frac{12}{5}$
Question : The income of A is $\frac{2}{3}$ of B's income and the expenditure of A is $\frac{3}{4}$ of B's expenditure. If $\frac{1}{3}$ of the income of B is equal to the expenditure of A, then the ratio of the savings of A to those of B is:
Option 1: 5 : 3
Option 2: 3 : 5
Option 3: 4 : 3
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