Question : If $1 \frac{1}{3} \div \frac{2}{5} \times \frac{x}{5}=1 \frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$, then the value of $x$ is:
Option 1: 5.5
Option 2: 7.5
Option 3: 7.0
Option 4: 15
Correct Answer: 7.5
Solution :
Given expression,
$1 \frac{1}{3} \div \frac{2}{5} \times \frac{x}{5}=1 \frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$
⇒ $\frac{4}{3} \div \frac{2}{5} \times \frac{x}{5}= \frac{5}{4} \times \frac{2}{3} \div \frac{1}{6}$
Using the BODMAS Rule,
B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction
⇒ $\frac43\times\frac52\times\frac{x}5=\frac{5}{4}\times\frac23\times6$
⇒ $\frac{2x}{3}=5$
⇒ $x=\frac{15}{2}=7.5$
Hence, the correct answer is 7.5
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