$\frac{3}{7}$ of $\frac{5}{4}$ of $3024 = x$ [SBI—Jr. Associates (Pre.) Exam, 2016]

### Concept & Consecutive Fractions When finding a fraction "of" a fraction "of" a number, it translates to a continuous multiplication sequence. $$ \text{Value} = A \times B \times C $$ ### Step-by-Step Solution * **Given expression:** $\frac{3}{7} \times \frac{5}{4} \times 3024$ * Combine the fractions first to simplify the multiplication: * $\frac{3 \times 5}{7 \times 4} = \frac{15}{28}$ * Now, the expression is: $\frac{15}{28} \times 3024$ * Divide 3024 by 28. To do this easier, divide by 4 first, then by 7: * $\frac{3024}{4} = 756$ * $\frac{756}{7} = 108$ * Now, multiply the remaining factors: * $15 \times 108$ * Calculate: $15 \times 100 = 1500$, and $15 \times 8 = 120$. * $1500 + 120 = 1620$. ### Exam Strategy & Shortcut Look at the unit digits. $15 \times 108$: The unit digit of $5 \times 8$ is 0. However, all options end in 0. Let's look at the approximate value: $15 \times 100 = 1500$. Since $108 > 100$, the answer must be greater than 1500. Only one option fits this criteria. ### Common Pitfall Trying to multiply 3024 by the numerators (3 and 5) before dividing can lead to very large numbers, increasing the chance of calculation errors. Always divide (cancel out) first. ### Final Answer Therefore, the correct answer is **1620**.