Model 4 Time & Distance with Ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Let the distance of destination be D km

Let the speed of A = 3x km/hr

then speed of B = 4x km/hr

According to question,

$D/{3x} - D/{4x}$ = 30 minutes = $1/2$ hr

= $D/{12x} = 1/2$

$D/{3x} = 4/2$ = 2 hours

Hence, time taken by A to reach destination = 2hrs.

Here, $S_1 = 3x, S_2 = 4x$

$t_2 = y, t_1 = y + 30/60 = y + 1/2$

$S_1t_1 = S_2t_2$

$3x × (y + 1/2) = 4x × y$

$3y + 3/2 = 4y ⇒ y = 3/2$

Time taken by A

= $3/2 + 1/2$ = 2 hrs.

Answer: (d)

Using Rule 1,

Let speed of cyclist = x kmph

& Time = t hours

Distance = ${xt}/2$ while time = 2t

∴ Required ratio = ${xt}/{2 × 2t}$ : x = 1 : 4

Answer: (a)

AC = Distance covered by train starting from A in 3 hours

= 50 × 3 = 150 km

BC = Distance covered by train starting from B in 2 hours

= 60 ×2 = 120 km

∴ AC : BC = 150 : 120 = 5 : 4