Question

te present ages of A and B is 4:5 .18 yrs ago this ratio was 11:16 .The sum of the present ages is​

Answer 1

Required Answer :

The sum of present ages of A and B = 90 years

Given :

• Ratio of the present ages of A and B = 4 : 5
• The ratio of their ages, 18 years ago = 11 : 16

To find :

• Sum of the present ages of A and B

Solution :

Let,

• Present age of A = 4x
• Present age of B = 5x

Their ages 18 years ago,

⇒ Age of A = 4x - 18 years

⇒ Age of B = 5x - 18 years

According to the question,

⇒ Age of A/Age of B = 11/16

⇒ (4x - 18)/(5x - 18) = 11/16

⇒ 16(4x - 18) = 11(5x - 18)

⇒ 64x - 288 = 55x - 198

⇒ 64x - 55x = - 198 + 288

⇒ 9x = 90

⇒ x = 90/9

⇒ x = 10

Substituting the value of x in the present ages of A and B :

⇒ Present age of A = 4x

⇒ Present age of A = 4(10)

⇒ Present age of A = 40 years

⇒ Present age of B = 5x

⇒ Present age of B = 5(10)

⇒ Present age of B = 50 years

The sum of present ages of A and B :

⇒ 40 + 50

⇒ 90 years

Therefore,

• The sum of present ages of A and B = 90 years

Answer 2

Answer:

• The sum of their present ages is 90 years

Step-by-step explanation:

Given:

• The present ages of A and B are in the ratio 4 : 5
• 18 years ago the ratio of their ages was 11 : 16

To Find:

• The resultant sum of their present ages

Assumptions:

• Let A's present age be 4x
• Let B's present age be 5x

According to the question:

$\longrightarrow \tt \dfrac{4x- 18}{5x- 18} = \dfrac{11}{16}$

By cross multiplying :

$\longrightarrow \tt 16 ( 4x - 18 )= 11 ( 5x - 18 )$  

$\longrightarrow \tt 64x -228 = 55x - 198$

$\longrightarrow \tt 64x - 55x = -198 + 225$

$\longrightarrow \tt 9x = -198 + 288$

$\longrightarrow \tt 9x = 90$

$\longrightarrow \tt x = \cancel\dfrac{90}{9}$

$\longrightarrow {\blue{\boxed{\frak{ x = 10 }}}\pink\bigstar}$

Present ages of A will be :

→ The present age of A  = 4x

→ The present age of A = 4 ( 10 )

→ The present age of  A =  40 years

Present ages of B will be :

→ The present age of B  = 5x

→ The present age of B  = 5(10)

→ The present age of B  = 50 years

Sum of the Present ages of them will be :

→ The sum of their present ages = 4x + 5x

→ The sum of their present ages = 40 + 50

→ The sum of their present ages = 90 years

Therefore :

• The sum of the present ages of A and B = 90 years

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