Question

Two numbers are in the ratio 9:16. If each number increased by 15, then the ratio becomes 2:3. The number are​

Answer 1

$\huge{\boxed{\sf{\red{Given:}}}}$

Two numbers are in ratio 9:16

$\huge{\boxed{\sf{\pink{To\ find:}}}}$

The numbers

$\star \underline{\green{\rm{According\ to\ question,}}}$

If both the numbers are increased by 15 then the ratio becomes 2:3

So,

The equation formed is

$\boxed{\blue{\implies \frac{9+15}{16+15}= \frac{2}{3}}}$

[By cross multiplication, we get]

⇒ 3 * (9x + 15) = 2 * (16x + 15)

⇒ 27x + 45 = 32x + 30

⇒ 45 - 30 = 32x - 27x

[By transporting 30 to LHS and 27x to RHS]

⇒ 15 = 5x

⇒ 15 ÷ 5 = x

[By taking 5 to LHS]

∴ The value of x is 3

Now,

The two numbers are

• 9x = 9 * 3 = 27
• 16x = 16 * 3 = 48

Two numbers = 27 and 48

Answer 2

Answer:

(9x+15)/(16x+15) = 2/3

:

3(9x+15) = 2(16x+15)

:

27x +45 = 32x +30

:

5x = 15

:

x = 3

:

9(3) = 27

:

16(3) = 48

:

27/48 is original fraction

:

27 -12 = 15

:

48 -12 = 36

:

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15/36 = 5/12 is the new ratio

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Step-by-step explanation:

hope this will help you!!!