Question

A and B start at the same time from two places 30 km apart. If they walk in the same direction, A overtakes B in 10 hours and if they walk in opposite directions they meet in 2 hours. Find the rate of walking of A.

• A. 5 kmph
• B. 7 kmph
• C. 9 kmph
• D. 11 kmph
• E. 13 kmph

Answer 1

The correct option is C

9 kmph

Let the two places P₁ and P₂ be 30 km apart and let A start from P₁ and B from P₂.

Let A’s speed of walking be x km/hr and B’s speed by y km/hr. According to the question, when they walk in the same direction .

10 (x – y) = 30 …(i)

When they walk in opposite direction

2(x + y) = 30 …(ii)

On dividing (i) by (ii), we get

$\frac{5(x-y)}{x+y}=1\Rightarrow 5x-5y=x+y\Rightarrow 4x-6y=0...........\left(iii\right)$

On multiplying (ii) by 2, we get

4x+4y=60 ........................(iv)

$\Rightarrow$ - 6y - 4y = - 60

$\Rightarrow$ -10y = - 60

$\Rightarrow$ y = 6

On substituting value of y in (iv)

$\Rightarrow$ 4x + 4$\times$6 = 60

$\Rightarrow$ 4x+24=60

$\Rightarrow$ 4x=36

$\Rightarrow$ x=$\frac{36}{4}$=9

$\therefore$ A’s speed = 9 km/hr and B’s speed = 6 km/hr.