Question

37. A father and son start from A at 12kmph and 18kmph
respectively and reaches point B. if the son starts 60
mins after his father but reached 60 minutes before
him. Then what is the distance between A and B ?
1) 90 km
2) 72 km 3) 36 km
4) 42 km 5) None of these.​

Answer 1

To Find:-

• Find the distance between A and B.

Given:-

• A father and son start from A at 12kmph and 18kmph respectively and reaches point B. if the son starts 60 mins after his father but reached 60 minutes before him.

Solution:-

According to Question:-

$\tt\implies \: \dfrac { x } { 12 } - \dfrac { x } { 18 } = 2$

$\tt\implies \: \dfrac { 3x - 2x } { 36 } = 2$

$\tt\implies \: \dfrac { x } { 36 } = 2$

$\tt\implies \: x = 2 \times 36$

$\tt\implies \: x = 72 \: \: k \: m$

Hence,

Distance between A and B is 72 km.

Answer 2

Given Question :-

• A father and son start from A at 12kmph and 18kmph respectively and reaches point B. if the son starts 60 mins after his father but reached 60 minutes before him. Then what is the distance between A and B ?

$\large\underline\purple{\bold{Solution :- }}$

Given that

• Speed of father = 12 km/hr.

• Speed of son = 18 km/hr

• Son starts 60 minutes later after his father starts but reaches 60 minutes earlier than his father.

To Find :-

• Distance between A and B.

Calculation :-

• Let suppose that Distance between A and B is 'x' km.

So,

• time taken by father to travel 'x' km at a speed of 12 km/hr is given by

$\rm :\implies\: \boxed{ \pink{ \bf \: t_1\: = \tt \:\dfrac{x}{12} }}$

Now,

• time taken by son to travel 'x' km at a speed of 18 km/hr is given by

$\rm :\implies\: \boxed{ \pink{ \bf \: t_2 \: = \tt \: \dfrac{x}{18} }}$

• According to statement, we have

$\rm :\implies\:t_1 - t_2 = 2$

$\rm :\implies\:\dfrac{x}{12} - \dfrac{x}{18} = 2$

$\rm :\implies\:\dfrac{3x - 2x}{36} = 2$

$\rm :\implies\:\dfrac{x}{36} = 2$

$\rm :\implies\: \boxed{ \pink{ \bf \: x\: = \tt \:72 \: km }}$

So,

• Distance between A and B is 72 km.