Question

Seven years ago A was 4 times as old as B was then. Seven years hence,, A will be twice as old as B
will be then. Find the present age of each.

Answer 1

GIVEN:

• Seven years ago A was 4 times as old as B was then.
• Seven years hence,, A will be twice as old as B

TO FIND:

• What are the present ages of A and B ?

SOLUTION:

CASE :- 1)

Seven years ago A was 4 times as old as B was then

• A's age = (A –7)
• B's age = (B –7)

According to question:-

$\sf{\longmapsto (A-7) = 4(B-7) }$

$\sf{\longmapsto A-7 = 4B - 28}$

$\sf{\longmapsto A-4B = -28 + 7}$

$\bf{\longmapsto A -4B = -21...1)}$

$\sf{\longmapsto A = -21 + 4B }$

CASE :- 2)

Seven years hence, A will be twice as old as B

• A's age = (A+7)
• B's age = (B +7)

According to question:-

$\sf{\longmapsto (A+7) = 2(B+7) }$

$\sf{\longmapsto A+7 = 2B +14 }$

$\sf{\longmapsto A- 2B = 14-7}$

$\bf{\longmapsto A - 2B = 7....2) }$

Put the value of A from equation 1) in equation 2)

$\sf{\longmapsto -21+4B -2B = 7 }$

$\sf{\longmapsto 2B = 7+21 }$

$\sf{\longmapsto 2B = 28 }$

$\sf{\longmapsto B = \cancel\dfrac{28}{2} }$

$\bf{\longmapsto B = 14 }$

Put the value of B in equation 2)

$\sf{\longmapsto A - 2 \times 14 = = 7 }$

$\sf{\longmapsto A -28 = 7}$

$\sf{\longmapsto A = 7+28 }$

$\bf{\longmapsto A = 35 }$

❝ Hence, the present ages of A and B are 35 and 14 ❞

______________________

Answer 2

$\huge\underline\bold\red{Answer}$

Given :-

• Seven years ago A was 4 times as old as B was then.

• Seven years hence, A will be twice as old as B.

To Find :-

• Present age of each.

__________________________

Case 1)

Seven years ago A was 4 times as old as B then

• age of A => A - 7

• age of B => B - 7

According to question,

A - 7 = 4 ( B - 7 )

=> A - 7 = 4B - 28

=> A - 4B = - 28 + 7

=> A = - 21 + 4B ______1)

__________________________

Case 2)

Seven years hence, A will be twice as old as B.

• age of A = A + 7

• age of B = B + 7

According to question,

A + 7 = 2 ( B + 7 )

=> A + 7 = 2B + 14

=> A - 2B = 14 - 7

=> A - 2B = 7 ______2)

__________________________

Put the value of A in 2nd equation

Then,

- 21 + 4B - 2B = 7

=> - 21 + 2B = 7

=> 2B = 7 + 21

=> 2B = 28

=> B = 14

__________________________

Put the value of B in 2nd equation

Then,

A - 2(14) = 7

=> A - 28 = 7

=> A = 7 + 28

=> A = 35

Hence, the present ages of A and B are 35 and 14 respectively.

__________________________