Question

Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B What is the present age of A ?

Answer 1

Given

Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B

To find

Find the present age of A

Solution

★ Let A's age be x and B's age be y

**According to the given condition**

• Five years ago
• A's age = x - 5
• B's age = y - 5

➨ (x - 5) = 3(y - 5)

➨ x - 5 = 3y - 15

➨ x - 3y = -15 + 5

➨ x - 3y = -10 ---(i)

• Ten years later
• A's age = x + 10
• B's age = y + 10

➨ (x + 10) = 2(y + 10)

➨ x + 10 = 2y + 20

➨ x - 2y = 20 - 10

➨ x - 2y = 10 ---(ii)

✑ Subtract both the equations

➨ (x - 3y) - (x - 2y) = -10 - 10

➨ x - 3y - x + 2y = -20

➨ - y = -20

➨ y = 20

✑ Putting the value of y in eqⁿ (i)

➨ x - 3y = -10

➨ x - 3*20 = -10

➨ x - 60 = -10

➨ x = 60 - 10

➨ x = 50

Hence,

Present age of A = x = 50 yrs

Present age of B = y = 20 yrs

Answer 2

GIVEN:

• Five years ago, A was thrice as old as B
• Ten years later, A shall be twice as old as B

TO FIND:

• What is the present age of A ?

SOLUTION:

✪ Case 1 ✪

☞ Five years ago, A was thrice as old as B

• A's age = (A-5)
• B's age = (B-5)

According to given conditions:-

$\rm{\dashrightarrow (A-5) = 3(B-5) }$

$\rm{\dashrightarrow A - 5 = 3B - 15 }$

$\rm{\dashrightarrow A - 3B = -15+5 }$

$\bf{\dashrightarrow A - 3B = -10....1) }$

$\rm{\dashrightarrow A = -10 + 3B }$

✪ Case 2 ✪

☞ ten years later, A shall be twice as old as B

• A's age = (A + 10)
• B's age = (B + 10)

According to given conditions:-

$\rm{\dashrightarrow (A+10) = 2(B+10)}$

$\rm{\dashrightarrow A+10 = 2B + 20 }$

$\rm{\dashrightarrow A - 2B = 20-10}$

$\bf{\dashrightarrow A -2B = 10....2) }$

Now, put the value of 'A' from equation 1) in equation 2)

$\rm{\dashrightarrow (-10+3B) -2B = 10 }$

$\rm{\dashrightarrow -10+3B -2B = 10 }$

$\rm{\dashrightarrow 3B-2B = 10 + 10}$

$\bf{\dashrightarrow B = 20 \: years}$

Put the value of 'B' in equation 1)

$\rm{\dashrightarrow A - 3 \times 20 = -10 }$

$\rm{\dashrightarrow A -60 = -10 }$

$\rm{\dashrightarrow A = -10 + 60 }$

$\bf{\dashrightarrow A = 50 \: years }$

❝ Hence, the present age of 'A' is 50 years and that of 'B' is 20 years ❞

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