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

Question : 6 [SSC MTS 2013]

A cyclist, after cycling a distance of 70 km on the second day, finds that the ratio of distance covered by him on the first two days is 4 : 5. If he travels a distance of 42 km. on the third day, then the ratio of distance travelled on the third day and the first day is :

a) 3 : 2

b) 3 : 4

c) 2 : 3

d) 4 : 3

Answer: (b)

Using Rule 1,

Distance covered on the first day

= $4/5 × 70$ = 56 km

∴ Required ratio = 42 : 56 = 3 : 4

Question : 7 [SSC CGL Prelim 2007]

A and B run a 5 km race on a round course of 400 m. If their speed are in the ratio 5 : 4, the number of times, the winner passes the other, is

a) 2

b) 3

c) 5

d) 1

Answer: (b)

The winner will pass the other, one time in covering 1600m.

Hence, the winner will pass the other 3 times in completing 5km race.

Question : 8 [SSC CGL Prelim 2007]

The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination ?

a) 2 hours

b) 2$2/3$ hours

c) 1$2/3$ hours

d) 1$1/3$ hours

Answer: (d)

Ratio of speed = 3 : 4

Ratio of time taken = 4 : 3

Let the time taken by A and B be 4x hours and 3 x hours respectively.

Then, $4x - 3x = 20/60 ⇒ x = 1/3$

Time taken by A = 4x hours

= $(4 × 1/3)$ hours = 1$1/3$ hours

Using Rule 9,

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

$t_2 = y, t_1 = y + 20/60 = y + 1/3$

$S_1t_1 = S_2t_2$

$3x(y + 1/3) = 4xy$

3y + 1 = 4y, y = 1

∴ Time taken by A

= 1 + $1/3 = 1{1}/3$ hours

Question : 9 [SSC CGL Prelim 2007]

The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6 : 5. The ratio of time taken by them to cross a pole is

a) 11 : 8

b) 25 : 18

c) 27 : 16

d) 5 : 6

Answer: (b)

Required ratio

= $5/6 : 3/5$

${30 × 5}/6 : {30 × 3}/5$ = 25 : 18

Question : 10 [SSC CGL Tier-I 2016]

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is :

a) 3 : 4

b) 4 : 3

c) 4 : 5

d) 3 : 5

Answer: (a)

Let the speed of train be x kmph. and the speed of car be y kmph.

Time = $\text"Distance"/ \text"Speed"$

According to the question,

$120/x + 480/y$ = 8

$15/x + 60/y$ = 1 ...(i)

and, $200/x + 400/y = 25/3$

$8/x + 16/y = 1/3$

$24/x + 48/y$ = 1 ...(ii)

From equations (i) and (ii),

$24/x + 48/y = 15/x + 60/y$

$24/x - 15/x = 60/y - 48/y$

$9/x = 12/y$

$x/y = 9/12 = 3/4$ = 3 : 4

IMPORTANT quantitative aptitude EXERCISES

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