Question Detail

What fraction of \begin{aligned} \frac{4}{7}\end{aligned} should be added to itself to become \begin{aligned} 1\frac{1}{14} \end{aligned}

\begin{aligned} \frac{7}{8} \end{aligned}
\begin{aligned} \frac{7}{9} \end{aligned}
\begin{aligned} \frac{7}{10} \end{aligned}
\begin{aligned} \frac{7}{11} \end{aligned}

Answer: Option A

Explanation:

\begin{aligned}
=> \frac{4}{7}x + \frac{4}{7} = \frac{15}{4}
\end{aligned}
\begin{aligned}
= \frac{4}{7}x = \frac{15}{4} - \frac{4}{7}
\end{aligned}
\begin{aligned}
= \frac{4}{7}x = \frac{7}{14}
\end{aligned}
\begin{aligned}
= x = \frac{1}{2}\times \frac{7}{4} = \frac{7}{8}
\end{aligned}

1. (3080 + 6160) / 28

Answer: Option C

Explanation:

As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9240)/28 = 330

2. Simplify
\begin{aligned} 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{7}+\frac{1}{14}+\frac{1}{28} = ? \end{aligned}

Answer: Option A

Explanation:

By taking LCM we get
=\begin{aligned} \frac{28+14+7+4+2+1}{28}
= \frac{56}{28} = 2\end{aligned}

3. If a - b = 3 and \begin{aligned} a^2 + b^2 = 29 \end{aligned}, then find the value of ab

Answer: Option C

Explanation:

Remember the formula, if not then cram it :)
\begin{aligned} 2ab = (a^2 + b^2)- (a-b)^2 \end{aligned}
=> 2ab = 29 - 9 = 20
=> ab = 10

4. Simplify
\begin{aligned}
\frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} } \div 5.25
\end{aligned}

\begin{aligned} \frac{3}{5} \end{aligned}
\begin{aligned} \frac{3}{6} \end{aligned}
\begin{aligned} \frac{3}{7} \end{aligned}
\begin{aligned} \frac{3}{8} \end{aligned}

Answer: Option C

Explanation:

\begin{aligned}
\frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} }\div 5.25
\end{aligned}

\begin{aligned}
= \frac{\frac{7}{2}\times {\frac{2}{5}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{15}{4}}}\div 5.25
\end{aligned}

\begin{aligned}
= \frac{\frac{21}{10}}
{\frac{7}{2} \times { \frac{4}{15}}}\div {\frac{525}{100}}
\end{aligned}

\begin{aligned}
= \frac{21}{10}\times{\frac{15}{14}}\times\frac{100}{525}

= \frac{6}{14}
= \frac{3}{7}
\end{aligned}

5. The number of girls in a class are 7 times the number of boys, which value can never be the of total students

Answer: Option D

Explanation:

Let the boys are X, then girls are 7X, total = X+7X = 8X

So it should be multiple of 8, 30 is not a multiple of 8.

Question Detail

What fraction of \begin{aligned} \frac{4}{7}\end{aligned} should be added to itself to become \begin{aligned} 1\frac{1}{14} \end{aligned}

1. (3080 + 6160) / 28

2. Simplify \begin{aligned} 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{7}+\frac{1}{14}+\frac{1}{28} = ? \end{aligned}

3. If a - b = 3 and \begin{aligned} a^2 + b^2 = 29 \end{aligned}, then find the value of ab

4. Simplify \begin{aligned} \frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} } \div 5.25 \end{aligned}

5. The number of girls in a class are 7 times the number of boys, which value can never be the of total students

2. Simplify
\begin{aligned} 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{7}+\frac{1}{14}+\frac{1}{28} = ? \end{aligned}

4. Simplify
\begin{aligned}
\frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} } \div 5.25
\end{aligned}