Question

give correct answer. ​

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

✧$\huge \mathcal \red {\underline{\underline{A}}}$ $\huge \mathcal \green {\underline{\underline{N}}}$ $\huge \mathcal \pink {\underline{\underline{S}}}$ $\huge \mathcal \blue {\underline{\underline{W}}}$ $\huge \mathcal \orange {\underline{\underline {E}}}$ $\huge \mathcal \purple {\underline{\underline{R}}}$✧

❥︎ Given :

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

❥︎ To find :

The numbers

❥︎ Solution :

• Let the number be 9x and 16x

• In fraction,

→ $\frac {9x}{16x}$

• If each number increased by 15, then the fraction becomes,

→ $\frac {9x + 15}{16x + 15}$

• According to the question, the ratio becomes 2:3, then equation will be,

→ $\frac {9x + 15}{16x + 15} = \frac {2}{3}$

• Now, we can solve this equation by doing cross multiplication.

→ $\frac {9x + 15}{16x + 15} = \frac {2}{3}$

→ $3(9x + 15) = 2(16x + 15)$

→ $27x + 45 = 32x + 30$

→ $45 - 30 = 32x - 27x$

→ $15 = 5x$

→ $\frac {15}{5} = x$

→ $3 = x$

• Now, we can find the numbers by putting the value of x.

→ $9x = 9 × 3 = 27$

→ $16x = 16 × 3 = 48$

$\bold \therefore \fbox \textsf {Hence, the two numbers are 27 and 48.}$

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