# If (5x–2y) : (x–2y) = 9 : 17, then find the

value of 9x/13y
.

यदि (5x–2y) : (x–2y) = 9 : 17, तो 9x/13y का मान ज्ञात कीजिए ।

#

(a) 72/421 (b) 151/ 1731

(c) 144/1001 (d) 36/247

SSC GD 2022 TIER-1

### Solution :

We are given a ratio: (5x - 2y) : (x - 2y) = 9 : 17

We need to find the value of 9x / 13y

**Cross-multiplication:**Ratios represent proportions, so we can cross-multiply: (5x - 2y) * 17 = 9 * (x - 2y)**Simplify:**Expand the equation: 85x - 34y = 9x - 18y**Solve for x/y:**Combine like terms and solve for x/y: 76x = 16y x/y = 16/76 = 4/19**Substitute into 9x/13y:**We're asked for the value of 9x/13y. Substitute our x/y result: 9x/13y = (9 * 4) / (13 * 19) = 36/247

**Answer:**

Therefore, the value of 9x/13y is **(d) 36/247**.

*Speed Math Solution (with explanation) : *

Given $\frac{5\ufffd-2\ufffd}{\ufffd-2\ufffd}=\frac{9}{17}$

.

We immediately observe that $5\ufffd-2\ufffd$ and $\ufffd-2\ufffd$ have a common factor of $(\ufffd-2\ufffd)$ in both numerator and denominator. Canceling this common factor, we're left with $\frac{5\ufffd}{1}=\frac{9}{17}$.

From this, we can quickly determine that $\ufffd=\frac{9}{17}\times 5=\frac{45}{17}$.

Now, we need to find $\frac{9\ufffd}{13\ufffd}$. $\frac{9\ufffd}{13\ufffd}=\frac{9\times \frac{45}{17}}{13\ufffd}=\frac{9\times 45}{13\times 17}=\frac{9\times 9\times 5}{13\times 17}=\frac{36}{247}$

So, the value of $\frac{9\ufffd}{13\ufffd}$ is $\frac{36}{247}$, which corresponds to option (d).

Thank You !