Evaluate: {1}{(2/3)+(3/5)}÷ 8/39

Correct Answer is : 31291523129/1523152129

Correct Answer is : 31291523129/1523152129

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RRB Technician Grade I 19 Dec 2024 Shift 2 Paper

Question : 60 of 100

Marks: +1, -0

Evaluate:

\frac{1}{(\frac{2}{3})+(\frac{3}{5})}\div \frac{8}{39}

Solution:

Concept:

Use BODMAS rule and multiply by the reciprocal while dividing fractions.

Explanation:

First solve the denominator

\frac{2}{3}+\frac{3}{5}

LCM of 3 and 5 is 15.

\frac{2}{3}+\frac{3}{5}=\frac{10+9}{15}=\frac{19}{15}

The expression becomes

\frac{1}{\frac{19}{15}}\div \frac{8}{39}

\frac{1}{\frac{19}{15}}=\frac{15}{19}

Now, dividing by

\frac{8}{39}

means multiplying by

\frac{39}{8}

\frac{15}{19}\times \frac{39}{8}=\frac{585}{152}

Convert

\frac{585}{152}

to a mixed fraction:

585 \div 152

gives quotient 3 and remainder 129.

So,

\frac{585}{152}=3\frac{129}{152}

Answer:

Option C:

3\frac{129}{152}

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