Question : A school group charters three identical buses and occupies $\frac{4}{5}$ of the seats. After $\frac{1}{4}$ of the passengers leave, the remaining passengers use only two of the buses. The fraction of the seats on two buses that are now occupied is:
Option 1: $\frac{8}{9}$
Option 2: $\frac{7}{10}$
Option 3: $\frac{7}{9}$
Option 4: $\frac{9}{10}$
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Correct Answer: $\frac{9}{10}$
Solution : Let the number of seats in each bus be $x$. According to the question, The total number of seats in the three buses is $3 × x = 3x$. Total passengers = $3x × \frac{4}{5} =\frac{12x}{5}$. $\frac{1}{4}$ of the total passengers leave the bus. Remaining passengers = $\frac{12x}{5}\times\frac{3}{4}=\frac{36x}{20}$ So, the fraction of the seats on the two buses that are now occupied is: $\frac{36x}{20}\times\frac{1}{2x}=\frac{9}{10}$ Hence, the correct answer is $\frac{9}{10}$.
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Question : Which fraction among the following is the least? $\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}$
Option 1: $\frac{5}{11}$
Option 2: $\frac{7}{12}$
Option 3: $\frac{9}{17}$
Option 4: $\frac{8}{13}$
Question : The sum of three fractions is $2\frac{11}{24}$. On dividing the largest faction by the smallest fraction, $\frac{7}{6}$ is obtained which is $\frac{1}{3}$ greater than the middle fraction. The smallest fraction is:
Option 1: $\frac{5}{8}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{3}{7}$
Question : Find the fraction which bears the same ratio to $\frac{1}{27}$ that $\frac{3}{7}$ does to $\frac{5}{9}$.
Option 1: $\frac{5}{9}$
Option 2: $\frac{1}{35}$
Option 3: $\frac{45}{7}$
Option 4: $\frac{7}{45}$
Question : Raju ate $\frac{3}{8}$th part of a pizza and Adam ate $\frac{3}{10}$th part of the remaining pizza. Then Renu ate $\frac{4}{7}$th part of the pizza that was left. What fraction of the pizza is still left?
Option 1: $\frac{5}{12}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{8}$
Option 4: $\frac{3}{16}$
Question : The sum of three numbers is 2, the 1st number is $\frac{1}{2}$ times the 2nd number and the 3rd number is $\frac{1}{4}$ times the 2nd number. The 2nd number is:
Option 1: $\frac{7}{6}$
Option 2: $\frac{8}{7}$
Option 3: $\frac{9}{8}$
Option 4: $\frac{10}{9}$
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