Quant Boosters  Maneesh  Set 2

Let speed of Man is S
Relative speed = 16+S
15 minutes = 1/4 hour
Trains are 16/4 = 4 km apart
So 4 = (16+S) * 1/5
S = 2016 = 4 kmph

Q5) Ravi takes 40 seconds to walk up on an escalator which is moving upwards but he takes 60 seconds to walk up on an escalator which is moving downwards. How much time will he take to walk up if the escalator is not moving?

Let speed of Ravi r and speed of escalator is x
When both are moving up, effective speed (r+x)
When escalator moving down, Ravi moving up effective speed rx
When escalator not moving his speed r
Speeds (rx), r and (r+x) are in A P
so time taken when escalator is not moving will be HM of other two time.
Time taken when escalator is not moving = 24060/100 = 48 seconds

Q6) Ravi takes 60 seconds on an escalator which is moving down when he walks down but takes 40 seconds when he runs down. He takes 20 steps when he is walking whereas he takes 30 steps when he is running. What is the total number of steps in escalator ?

Let speed of escalator x steps/second
Distance covered by Ravi is same whether he walks or runs
20 + 60x = 30 + 40x
20x = 10
x = 1/2 steps/second
total number of steps = 20 + 60 * 1/2 = 50 steps

Q7) Ravi and Rakesh are climbing on a moving escalator that is going up. Ravi takes 10 seconds to reach the top but Rakesh takes 8 seconds to reach the top. Rakesh takes 4 steps whereas Ravi can take only 3 steps in one second. What is the total number of steps in Escalator?

Speed of escalator x steps/second
Distance covered by both is same
10(3+x) = 8(4+x)
x = 1 step/second
Number of steps = 10 * 4 = 40 steps.

Q8) Two swimmers started simultaneously from the beach to the south and other to the east. Two hours later the distance between them turned out to be 100 KM. Find the speed of faster swimmer knowing that speed of one of them was 75% of speed of other?

Let speed s. Distance travelled in 2 hours 2s
speed 3s/4 = > distance travelled in 2 hours = 3s/2
it will form a right angled triangle.
(3s/2)^2 + (2s)^2 = 100^2
9s^2/4 + 4s^2 = 100^2
S = 40KMPH

Q9) Two men A and B run a 4 km race on a circular course of ¼ KM. If their speeds are in the ratio of 5:4. How often does the winner pass the other?

When a completes 5 rounds B completes 4 rounds
So A will overtake B when he completes 5 round = > 5 * 1/4 = 5/4 km
So there are three 5/4 km in 4 KM
So A will pass B in 3 times.

Q10) The Howrah –puri express can move at 45 km/hr without its rake, and the speed is diminished by a constant that varies as the square root of the number of wagons attatched.If its known with 9 wagons the speed is 30 KM/HR what’s greatest number of wagons with which the train can just move?

S1/S2 = root ((W1/W2))
where S is change in speed and w is number of wagons
S1 = 4530 = 15
W1 = 9
S2 = 450 = 45
15/45 = 3/ROOT(W2)
W2 = 81
So if 81 wagons are there then train wont move
so answer is 80

Q11) A watch which gains uniformly is 2 minutes slow at noon on Sunday and is 4 minutes 48 seconds fast at 2 PM on the following Sunday. When was it correct?

From Sunday noon to following Sunday 2 PM = 170 hours
The watch gains 2+4+48/60 = 6+48/60 minutes or 6 4/5 minutes in 170 hours.
Watch will show correct time when it has gained 2 minutes.
The watch gains 2 minutes in 2*170/6 4/5 = 50 hours = > 2 days and 2 hours = > 2 PM Tuesday

Q12) If 30 men working 7 hours per day can do a work in 18 days. In how many days will 21 men working 8 hours a day do the same work?

Total work = 30 * 7 * 18
Total work is equal, hence 30 * 7 * 18 = 21 * 8 * x
Where x is the number of days required for 21 men to finish the work.
X = 30 * 7 * 18 / 21 * 8 = 22.5 days

Q13) Two men and 7 boys can do a piece of work in 14 days. 3 men and 8 boys can do it in 11 days. In how many days can 8 men and 6 boys do a work 3 times as big as the first?

2/M+7/B = 1/14 (Work done by 2 men and 7 boys In one day) …… (1)
3/M+8/B = 1/11 ………… (2)
(1) * 3 > 6/M + 21/B = 3/14 …….. (3)
(2) * 2 > 6/M+ 16/B = 2/11 ………. (4)
(3)(4) > 5/B = 5/154
1/B = 1/154 > One boy will take 154 days to complete the work.
2/M = 1/14 – 1/22 = 117/154 = 4/154
1/M = 2/154 = 1/77 > One man will take 77 days to complete the work.
In case of 8 men and 6 boys > 8/77 + 6/154 = 16+6/154 = 22/154
Number of days required for 8 men and 6 boys to complete the same work = 154/22 = 7 day
Since work is increased 3 times, required answer is 3*7 = 21 days.

Q14) To do a piece of work B takes 3 times as long as A and C together and C twice as long as A and B together. If the three together can complete the work In 10 days, how long would each take by himself?