Question

two number are in ratio 9 : 16 if 15 is added to each number the ratio becomes 2: 3 find the number ​

Answer 1

AnswEr :

• Ratio = 9 : 16
• If 15 is added to both, it will be 2 : 3
• Find the Numbers.

Let the Numbers be 9x and, 16x

• Let's Head to the Question Now :

↠ Ratio + 15 Each = New Ratio

↠ (9x + 15) : (16x + 15) = 2 : 3

• Product of Extreme = Product of Mean

↠ 3 × (9x + 15) = 2 × (16x + 15)

↠ 27x + 45 = 32x + 30

↠ 45 – 30 = 32x – 27x

↠ 15 = 5x

• Dividing both term by 5

↠ x = 3

• N U M B E R S :

◗ First Number = 9x = 9( 3 ) = 27

◗ Second Number = 16x = 16( 3 ) = 48

∴ Numbers will be 27 and 48 respectively.

━━━━━━━━━━━━━━━━━━━━━━━━

• V E R I F I C A T I O N :

⇒ Ratio + 15 Each = New Ratio

⇒ (9x + 15) : (16x + 15) = 2 : 3

⇒ 9(3) + 15 : 16(3) + 15 = 2 : 3

⇒ (27 + 15) : (48 + 15) = 2 : 3

⇒ 42 : 63 = 2 : 3

• Dividing 1st Ratio by 21

⇒ 2 : 3 = 2 : 3 ⠀⠀⠀⠀⠀⠀⠀Hence, Verified!

Answer 2

❏ $\huge{\underline{\underline{\mathbb{\blue{ANSWER}}}}}$

→ The two required numbers are 27 and 48 after adding 15 they will become 42 and 63

→ Solution

The ratio between 2 numbers is 9:16 we can also write it as $\frac{9}{15}$

Let the fraction as 9x/16x

After adding 15 to the numbers →

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

Cross multiplying these fractions →

→ 3( 9x + 15) = 2( 16x + 15)

→ 27 x + 45 = 32 x + 30

→ 45 - 30 = 32x - 27x

→ 15 = 5x

→ $\frac{15}{5}$ = x

→ 3 = x

So, we got the value of x here hence the numbers will be

$\mathbb \pink{9x = 9 \times 3 = 27}$

$\mathbb \pink{16x = 16 \times 3 = 48}$

After adding 15 we got :-

27 + 15 = 42

48 + 15 = 63

Verification →

Ratio of 27 to 48 is

$> \frac{27}{48}$

$> \frac{3(9)}{3(16)}$

$> \frac{9}{16}$

After adding 15

$> \frac{42}{63}$

$> \frac{21(2)}{21(3)}$

$> \frac{2}{3}$

Hence verified