Question

A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his
sister C. The age of D and C differ by 40 years. Find the ages of A and B.

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Answer 1

Let the Age of A be : P

Let the Age of B be : Q

●  A and B ages differ by 2 years

$\longrightarrow$  P - Q = 2 ---------- (1)

●  A's father D is twice as old as A

$\longrightarrow$  Age of A's Father (D) = 2P

●  B is twice as old as his Sister C

$\longrightarrow$ B's Sister C is half of the Age of B

$\mathrm{\longrightarrow C = \dfrac{Q}{2}}$

●  The Age of D and C differ by 40

$\longrightarrow$  D - C = 40

$\mathrm{\longrightarrow 2P - \dfrac{Q}{2} = 40}$

$\mathrm{\longrightarrow \dfrac{2(2P) - Q}{2} = 40}$

$\mathrm{\longrightarrow \dfrac{4P - Q}{2} = 40}$

$\mathrm{\longrightarrow {4P - Q} = 80\;-----\;(2)}$

Subtract Equation (1) from Equation (2)

$\longrightarrow$  [4P - Q] - [P - Q] = 80 - 2

$\longrightarrow$  4P - Q - P + Q = 78

$\longrightarrow$  3P = 78

$\longrightarrow$  P = 26

Substitute value of P in Equation (1)

$\longrightarrow$  26 - Q = 2

$\longrightarrow$  Q = 26 - 2

$\longrightarrow$  Q = 24

$\longrightarrow$  Ages of A and B are 26 and 24 respectively

Answer 2

Let the Age of A be : P

Let the Age of B be : Q

● A and B ages differ by 2 years

\longrightarrow⟶ P - Q = 2 ---------- (1)

● A's father D is twice as old as A

\longrightarrow⟶ Age of A's Father (D) = 2P

● B is twice as old as his Sister C

\longrightarrow⟶ B's Sister C is half of the Age of B

\mathrm{\longrightarrow C = \dfrac{Q}{2}}⟶C=

2

Q

● The Age of D and C differ by 40

\longrightarrow⟶ D - C = 40

\mathrm{\longrightarrow 2P - \dfrac{Q}{2} = 40}⟶2P−

2

Q

=40

\mathrm{\longrightarrow \dfrac{2(2P) - Q}{2} = 40}⟶

2

2(2P)−Q

=40

\mathrm{\longrightarrow \dfrac{4P - Q}{2} = 40}⟶

2

4P−Q

=40

\mathrm{\longrightarrow {4P - Q} = 80\;-----\;(2)}⟶4P−Q=80−−−−−(2)

Subtract Equation (1) from Equation (2)

\longrightarrow⟶ [4P - Q] - [P - Q] = 80 - 2

\longrightarrow⟶ 4P - Q - P + Q = 78

\longrightarrow⟶ 3P = 78

\longrightarrow⟶ P = 26

Substitute value of P in Equation (1)

\longrightarrow⟶ 26 - Q = 2

\longrightarrow⟶ Q = 26 - 2

\longrightarrow⟶ Q = 24

\longrightarrow⟶ Ages of A and B are 26 and 24 respectively