[Solved] If (5x–2y) : (x–2y) = 9 : 17, then find the value of 9x/13y (a) 72/421 (b) 151/ 1731 (c) 144/1001 (d) 36/247

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

 

1. Cross-multiplication: Ratios represent proportions, so we can cross-multiply: (5x - 2y) * 17 = 9 * (x - 2y)

2. Simplify: Expand the equation: 85x - 34y = 9x - 18y

3. Solve for x/y: Combine like terms and solve for x/y: 76x = 16y x/y = 16/76 = 4/19

4. 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 $\frac{5�-2�}{�-2�}=\frac{9}{17}$

.

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

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

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

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

Thank You !