Quant Boosters  Maneesh  Set 2

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?

3 times B’s daily work = (A+C)’s daily work
4 times B’s daily work = (A+B+C)’s daily work = 1/10
B’s daily work = 1/40
Hence B takes 40 days.
2 times C’s daily work = (A+B)’s daily work
3 times C’s daily work = (A+B+C)’s daily work = 1/10
C’s daily work = 1/30
Hence C takes 30 days to complete the work.
A’s daily work = 1/10 – (1/30+1/40) = 1/10 – 7/120 = 5/120 = 1/24
A takes 24 days to complete the work.

Q15) P can do a piece of work in 10 days, which Q can finish in 15 days. If they work at it on alternate days with P beginning In how many days the work will be finished.

The work done by P and Q in two days = 1/10+1/15 = 5/30 = 1/6
The work done in 12 days = 6/6 = 1
Hence work will be finished in 12 days.

Q16) Pipes A and B can fill a cistern in 20 and 30 minutes and C can empty it in 15 minutes. If the three are opened and closed one after the other successively for 1 min each in that order, how soon will the cistern be filled?

Part filled in 3 minutes = 1/20+1/30 – 1/15 = 3+24/60 = 1/60
Part filled in 165 minutes = 55/60
Part filled in 166 minutes = 55/60 + 1/20 = 58/60
Part filled in 167 minutes = 58/60+1/30 = 60/60 = 1
Hence it will be filled in 167 minutes.

Q17) A water tank is three fifth full. Pipe A can fill a tank in 8 minutes and pipe B can empty it in 5 minutes. If both the pipes are open how long will it take to empty/fill the tank completely?