Practice Problems with ratios - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) 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)
(b)
(c)
(d)
The winner will pass the other, one time in covering 1600m.
Hence, the winner will pass the other 3 times in completing 5km race.
Q-2) 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)
(b)
(c)
(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
Q-3) 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)
(b)
(c)
(d)
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
Q-4) 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)
(b)
(c)
(d)
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
Q-5) 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)
(b)
(c)
(d)
Using Rule 1,
Distance covered on the first day
= $4/5 × 70$ = 56 km
∴ Required ratio = 42 : 56 = 3 : 4
Q-6) 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)
(b)
(c)
(d)
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
Q-7) Two trains started at the same time, one from A to B and the other from B to A. If they arrived at B and A respectively 4 hours and 9 hours after they passed each other, the ratio of the speed of the two trains was
(a)
(b)
(c)
(d)
Using Rule 11,Time taken by 1st man to reach B after meeting 2nd man at C is '$t_1$' and time taken by 2nd man to reach A after meeting 1st man at C is '$t_2$' then:${\text"Speed of 1st man"(s_1)}/{\text"Speed of 2nd man"(s_2)} = √{t_2/t_1}$Distance from A to B = $s_1t_1 + S_2t_2$
Required ratio of the speed of two trains
= $√{9}/√{4} = 3/2$ or 3 : 2
Q-8) A car travels 80 km. in 2 hours and a train travels 180 km. in 3 hours. The ratio of the speed of the car to that of the train is :
(a)
(b)
(c)
(d)
Speed = $\text"Distance"/ \text"Time"$
∴ Speed of car : Speed of train
= $80/2 : 180/3$ = 40 : 60 = 2 : 3
Q-9) It takes 8 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)
(b)
(c)
(d)
Using Rule 1,
Speed of train = x kmph
Speed of car = y kmph
Case I,
$120/x + {600 - 120}/y$ = 8
$120/x + 480/y$ = 8
$15/x + 60/y$ = 1 ...(i)
Case II,
$200/x + 400/y$ = 8 hours 20 minutes
$200/x + 400/y = 8{1}/3$ hours = $25/3$
$8/x + 16/y = 1/3$
$24/x + 48/y$ = 1 ...(ii)
$15/x + 60/y = 24/x + 48/y$
$24/x - 15/x = 60/y - 48/y$
$9/x = 12/y$
$x/y = 9/12 = 3/4$ = 3 : 4
Q-10) A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speed is :
(a)
(b)
(c)
(d)
Using Rule 1,
Speed of truck = 550m/minute
Speed of bus = $33000/45$ m/minute
or $2200/3$ m/minute
Required ratio = 550 : $2200/3$
= $1 : 4/3 = 3 : 4$