Question

ten years ago a's age was half of B ' s age. if the ratio of their present age's is 3:4 , what Will be the sum of their presents ages​

Answer 1

35 years

Question states that 10 years ago A's age was ½ of B's age. If the ratio of their present ages is 3 : 4. & we're asked to calculate the sum of their present ages. So, first we've to find out their present ages. We've:

• Ten years ago A's age was ½ of B's age.
• & The ratio of the present age of A and B is 3 : 4.

Let's say, the present age of A be 3x and the present age of B be 4x.

» 10 years ago,

⠀⠀⠀⠀⌑ A's age = (3x – 10)

⠀⠀⠀⠀⌑ B's age = (4x – 10) ⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

• Ten years ago A's age was ½ of B's age. Writing it in a Linear equation:

↠⠀⠀3x – 10 = ½ × (4x – 10)

↠⠀⠀2(3x – 10) = (4x – 10)

↠⠀⠀6x – 20 = 4x – 10

↠⠀⠀6x – 4x = 20 – 10

↠⠀⠀2x = 10

↠⠀⠀x = ¹⁰⁄2

↠⠀⠀x = 5

⠀⠀

Therefore,

• The Present age of A = 3x = 3(5) = 15
• The Present age of B = 4x = 4(5) = 20

$\therefore$The present age of A and B is 15 and 20 years.

$\rule{230px}{.2ex}$

• S u m o f A G e s :

↠⠀⠀Sum = ( A's age + B's Age )

↠⠀⠀Sum = 15 + 20

↠⠀⠀Sum = 35

❝ Hence, sum of their ages is 35 years. ❞

Answer 2

Answer:

• 35 years.

Step-by-step explanation:

Given :

• Ten years ago, A's age was half of B's age.
• If the ratio of their present age's is 3 : 4.

To find :

• Sum of their present age's.

Solution :

Let the present age's of A and B be,

⇒ 3x

⇒ 4x

Their, ages 10 years ago will be,

⇒ 3x - 10

⇒ 4x - 10

According to the condition,

Ten year ago, A' age was half of B's age:

⇒ 3x - 10 = 1/2 × (4x - 10)

⇒ 3x - 10 = 2x - 5

⇒ x = - 5 + 10

⇒ x = 5

The present ages of A and B are,

⇒ 3x = 3(5) = 15 years

⇒ 4x = 4(5) = 20 years

Sum of their present age's of A and B are,

⇒ 3x + 4x

⇒ 15 + 20 = 35 years

Verification :

⇒ 3x - 10 = 1/2 × (4x - 10)

⇒ 3(5) - 10 = 1/2 × (4(5) - 10)

⇒ 15 - 10 = 1/2 × (20 - 10)

⇒ 5 = 1/2 × 10

⇒ 5 = 5

∴ L.H.S = R.H.S