Two men A and B walk from P to Q at a distanc | vedclass

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(D) Let the distance from $P$ to $R$ be $x 	ext{ km}$.Since both men start at the same time and meet at $R$,the time taken by $A$ to reach $R$ is equ

Vedclass · Accepted Answer

$18$

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(D) Let the distance from $P$ to $R$ be $x 	ext{ km}$.Since both men start at the same time and meet at $R$,the time taken by $A$ to reach $R$ is equal to the time taken by $B$ to reach $Q$ and then return to $R$.Time taken by $A$ to cover distance $PR = x 	ext{ km}$ at $3 	ext{ km/h}$ is $t_A = \frac{x}{3} 	ext{ hours}$.Time taken by $B$ to cover distance $PQ = 21 	ext{ km}$ and then $QR = (21 - x) 	ext{ km}$ at $4 	ext{ km/h}$ is $t_B = \frac{21 + (21 - x)}{4} = \frac{42 - x}{4} 	ext{ hours}$.Equating the times: $\frac{x}{3} = \frac{42 - x}{4}$.Cross-multiplying: $4x = 3(42 - x)$.$4x = 126 - 3x$.$7x = 126$.$x = \frac{126}{7} = 18 	ext{ km}$.

Two men $A$ and $B$ walk from $P$ to $Q$ at a distance of $21 \text{ km}$ at speeds of $3 \text{ km/h}$ and $4 \text{ km/h}$ respectively. $B$ reaches $Q$ and returns immediately and meets $A$ at $R$. The distance from $P$ to $R$ is (in $\text{km}$):

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