Question

2. The ratio of the numbers x and y is 2 : 3. If 9 is added to each number the
ratio becomes 3:4. Find the value of x and y.
(a) 18, 27 (b) 27, 18 (c) 9,6
(d) 6,9
11​

Answer 1

$\large{\frak{\red{Answer}}}$

$\sf{\pmb{\mathbb{\text{\blue{(a) 18, 27}}}}}$

${\large{\fbox{\red{Given}}}}$

The ratio of the numbers x and y is 2 : 3. If 9 is added to each number the ratio becomes 3:4. Find the value of x and y.

${\large{\pmb{\mathbb{\fbox{\red{Solution}}}}}}$

Let the numbers be ${\pmb{\mathbb{\text{\red{2x}}}}}$ and ${\pmb{\mathbb{\text{\red{3x}}}}}$

Let the new numbers in the ratio ${\pmb{\mathbb{\text{\red{3:4}}}}}$ be ${\pmb{\mathbb{\text{\red{3x}}}}}$ and ${\pmb{\mathbb{\text{\red{4x}}}}}$.

ATQ

2x + 9 + 3x + 9 = 3x + 4x

On solving the equation, we will get ${\pmb{\mathbb{\text{\red{x}}}}}$ as ${\pmb{\mathbb{\text{\red{9}}}}}$.

Hence, the two numbers in the ratio ${\pmb{\mathbb{\text{\red{2:3}}}}}$ are ${\pmb{\mathbb{\text{\red{18}}}}}$ and ${\pmb{\mathbb{\text{\red{27}}}}}$.

$\bf{\pmb{\mathbb{\fbox{\red{Hope it's help you}}}}}$