Quant Boosters  Maneesh  Set 2

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?

Tank’s 3/5 th part is filled .
In one minute 1/5 – 1/8 = 3/40 part will be removed
So number of minutes required to empty the tank = 3/5 *40/3 = 8 minutes.

Q18) Two pipes A and B can separately fill a cistern in 15 and 20 minutes respectively and waste pipe C can carry off 10 litres per minute. If all the pipes are opened when the cistern is full, it is emptied in 2 hours. How many litres does the cistern hold?