Question

the ratio if two number is 4:5 when 6 is added to each , ratio becomes 7:8 Find the numbers.​

Answer 1

★ Given :

• Two numbers are in ratio 4:5.
• After adding 6 to first number and 8 to second number the ratio becomes 7:8.

★ To Find :

• What are these two numbers ?

★ $olution :

Let x be the common in given ratios.

Therefore number becomes 4x and 5x

Here,

• First number = 4x
• Second number = 5x

Adding 6 to first number

• First Number = 4x+6

Adding 8 to second number

• Second Number = 5x+8

Now,

After adding 6 & 8 to both numbers the ratio becomes 7:8

• ⟼ (4x+6) : (5x+8) = 7:8
• ⟼ (4x+6) / (5x+8) = 7/8
• ⟼ 8(4x+6) = 7(5x+8)
• ⟼ 32x+48 = 35x+56
• ⟼ 48-56 = 35x-32x
• ⟼ -8 = 3x
• ⟼ x = -8/3

So,

• First Number = 4x = -8/3×4 = -32/3
• Second Number = 5x = -8/3×5 = -40/5

❥ H๏pε ¡т нεℓps uн !!

Answer 2

❖ Understanding The Question :

• There are two numbers which are in the ratio of 4 : 5 . If 6 is added to each of the numbers, their ratio becomes 7 : 8 . And we need to find the required numbers.

❖ Solution :

Lets assume the numbers as 4x and 5x .

Adding 6 to each of the ratio :

$\dashrightarrow \tt \: \dfrac{4x + 6}{5x + 6}$

Now, According to the question :

$\\ \dashrightarrow \tt \: \dfrac{4x + 6}{5x + 6} = \frac{7}{8}$

By doing cross multiplication we get :

$\\ \tt \: \dashrightarrow \: 7(5x + 6) = 8(4x + 6) \\ \\ \\ \tt \: \dashrightarrow \: 35x + 42 = 32x + 48 \\ \\ \\ \tt \: \dashrightarrow \: 35x - 32x = 48 - 42 \\ \\ \\ \tt \: \dashrightarrow \: 3x = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: \dashrightarrow \: x = \frac{6}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \dashrightarrow { \underline{ \boxed{ \mathfrak{ \pmb{ x = 2}}}}} \: \: \: \red{ \bigstar} \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence, The required numbers are :

• 4x = 4 × 2 = 8

• 5x = 5 × 2 = 10