If X: Y =3.2 then the value of

We are asked to find the value of

$\frac{2x + 5y}{3x + 7y}$

given that the ratio $X : Y = 3 : 2$.

Step 1: Express $x$ and $y$ in terms of a common variable

If $X : Y = 3 : 2$, let $x = 3k$ and $y = 2k$, where $k$ is any positive number.

Step 2: Substitute $x$ and $y$ into the expression

$\frac{2x + 5y}{3x + 7y} = \frac{2(3k) + 5(2k)}{3(3k) + 7(2k)}$

Step 3: Simplify numerator and denominator

Numerator: $2(3k) + 5(2k) = 6k + 10k = 16k$

Denominator: $3(3k) + 7(2k) = 9k + 14k = 23k$

Step 4: Simplify the fraction

$\frac{16k}{23k} = \frac{16}{23}$

✅ Answer: $\frac{16}{23}$