Model 4 Time & Distance with Ratios Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CPO S.I.2009]

Three cars travelled distance in the ratio 1 : 2 : 3. If the ratio of the time of travel is 3 : 2 : 1, then the ratio of their speed is

a) 1 : 3 : 9

b) 1 : 2 : 4

c) 4 : 3 : 2

d) 3 : 9 : 1

Answer: (a)

Required ratio = $1/3 : 2/2 : 3/1$

= $1/3$ : 1 : 3

$1/3$ × 3 : 1 × 3 : 3 × 3

[Since, Speed = $\text"Distance"/\text"Time"$]

= 1 : 3 : 9

Question : 2 [SSC CGL Prelim 1999]

In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :

a) 1$1/2$ hours

b) 2 hours

c) 2$1/2$ hours

d) 1 hour

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.

Using Rule 9,
Speed(s) ∝ $1/{time (t)}$ ⇒ s ∝ $1/t$
$s_1t_1 = s_2t_2$(Provided distance is constant)

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.

Question : 3 [SSC CGL Tier-II 2013]

A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is

a) 4 : 1

b) 1 : 2

c) 2 : 1

d) 1 : 4

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

Question : 4 [SSC CGL Prelim 2007]

A train starts from A at 7 a.m. towards B with speed 50 km/h. Another train starts from B at 8 a.m. with speed 60 km/h towards A. Both of them meet at 10 a.m. at C. The ratio of the distance AC to BC is

a) 5 : 4

b) 6 : 5

c) 4 : 5

d) 5 : 6

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

Question : 5 [SSC CGL Tier-I 2016]

A truck covers a distance of 550 metre in one minute where as a bus covers a distance of 33 km in $3/4$ hour. Then the ratio of their speeds is :

a) 2 : 3

b) 3 : 4

c) 1 : 4

d) 1 : 3

Answer: (b)

Speed of truck

= ${550\text"metre"}/{60\text"second"} = (55/6)$ m./sec.

Speed of bus

= ${33 × 1000 \text"metre"}/{3/4 × 60 × 60 \text"second"} = 440/36$ m./sec.

∴ Required ratio = $55/6 : 440/36$

= 55 × 6 : 440 = 3 : 4

IMPORTANT quantitative aptitude EXERCISES

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