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Study the paragraph and answer Q1 & Q2:

There are n taps numbered 1 to n, that can fill a tank, such that any tap (except the first) numbered i (in) working alone takes as much time to fill the empty tank as all the taps numbered less than i would take working together.

Q1. If the fourth tap takes 40 minutes to fill the tank when working alone then the eighth and the seventh tap would take how many minutes to fill the tank when working together

(1)  0.6 minutes (2) 1.66 minutes (3) 3.0 minutes (4) 3.33 minutes (5) None

Q2. If the 14th tap can fill the tank at the rate of 1427 litres per hour then the 15th tap will be able to fill the tank at a rate (in litres/hour) which is

(1) 66.66% more than 1427 litres/hour (2) 100% more than 1427 litres/hour(3) 166.66% more 1427 litres/hour (4) 111.11% more than 1427 litres/hour (5) None

Q3. Akash regularly makes a round trip up and down a river to meet his friend Rashmi. Today, his speed downstream is half his usual downstream speed while his speed upstream is double his usual upstream speed. If his usual speed in still water is 12 kmph and the usual stream speed is 8 kmph, how many hours (approximately) is he going to spend on today’s round trip of 40 km?

(1) 21/2    (2) 41/2       (3) 51/3        (4) 51/2        (5) None

Q4. In a box, there are 90 slips numbered from 1 to 90. Ramu picks up four slips at random one after the other without replacement. What is the probability that the numbers on the slips in the order he has picked up are ascending?

(1) 1/6 (2) 1/12 (3) 1/24 (4) 2/45 (5) 2/24

Q5. Two outlets of the same capacity when opened together can empty a full tank of volume 3000 cu.m in 24 hr. If the tank is going to be filled by a tap at the rate of 300 cu.m/hr, what is the least number of additional outlets (which have the same capacity as the former outlets) that have to be opened, so that the tank never overflows?

(1) 4 (2) 5 (3) 3 (4) 7 (5) 9

Q6. There are two water drums in my house whose volumes are in the ratio
1: 5. Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by the time I return from my college i.e. at 1.30 p.m., the smaller drum would just be full. But today I returned a little early and started drawing water from the well with the help of a bucket, poured one-third into the smaller drum and the remaining into the bigger drum. I continued this until the smaller drum was filled. Immediately after that, I shifted the pipe into the bigger drum and went for lunch. Today if the bigger drum was filled in 12 minutes before its normal time when was the smaller drum full?

(1) 1 : 18 p.m. (2) 1 : 28 p.m. (3) 1 : 26 p.m. (4) Cannot be determined. (5) 1 : 27 p.m

Q7. Two boats, travelling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?

(1) 1/12  (2) 1/6  (3) 1/4  (4) 1/3 (5) 2/3

Q8. Rahul and Rohit run a 100-metre race, where Rahul beats Rohit by 10 metres. To do a favour to Rohit, Rahul starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

(1) Rahul and Rohit reach the finishing line simultaneously.
(2)Rohit beats Rahul by 1 metre.
(3)Rohit beats Rahul by 11metres.
(4) Rahul beats Rohit by 1 metre
(5) None

Q9. If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15km/ hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

(1)  11 km/hr(2)  12 km/hr  (3)  13 Km/hr   (4) 14 Km/hr  (5) None

Q10. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

(1) 12 * 81(2) 16 * 192(3) 20 * 125  (4) 24 * 216  (5) None

Solution:

Q1. SOL:   2
If the fourth tap takes 40 minutes working alone then the first three taps together would take 40 minutes. Therefore, the fifth tap would take 20 minutes, the sixth 10 minutes, the seventh 5 minutes and the eighth 5/2 minutes. 8th and 7th together take = [1/(1/5 + 2/5)] = 5/3 = 1.66min

Q2. SOL:   2
The 15th tap can fill at a rate equal to the rate of 14th tap +
(rate of all taps from 1 to 14) = exactly twice the rate of the 14th tap.
∴100% more than 1427

Q3. SOL: 2
The new downstream speed = (12 + 8)/2 = 10 kmph
New upstream speed = (12 8) (2) = 8 kmph
Total time taken = 20/10 + 20/8= 2 + 5/2 = 4 ½

Q4.
SOL:  3
Since the slips are picked up one after the other without replacement, they have distinct numbers on them 4 distinct numbers can be arranged among themselves in 4! ways. (i.e., 24 ways). Of these 24 ways all of which are equally likely, only one arrangement is in ascending order.
∴The required probability = 1/24

Q5. SOL:     3

Two outlets can empty = 3000/24 or 125 cu.m/hr
The rate of inflow 300 cu.m/hr
The rate of outflow 125 cu.m/hr
Addition outflow required is 175 cu.m/hr
Hence at least 3 more outlets are needed.

Q6.
SOL:   3
The 12 minutes saved in filling the drums is because of my contribution of few buckets of water. I poured one-third of each bucket in the smaller drum and the remaining two-thirds in the bigger drum i.e. t min is saved in filling the smaller drum, 2t min is saved in filling the bigger drum.
3t = 12
t = 4
So, 4 min is saved by filling the smaller drum. So, the smaller drum was filled 4 minutes earlier than its normal
filling time. So, it was filled at 1: 26 p.m.

Q7. SOL:   3

Their relative speed is 15 km/h. They are 20 km apart hence in 80 min they will collide.
Now in 79 min distance covered by the first boat is 79/12 km and distance travelled by the second boat is 79/6 km so they are ¼ km apart.

Q8SOL:   4

Time in which Rahul travels 100 m Rohittravels only 90 m. Hence the ratio of their speeds is 10:9.
Time in which Rahul covers 110m, Rohit will cover 99m. Hence Rohit is beaten by 1 meter.

Q9. SOL:   2

In both, the cases distance covered is constant hence speed will be inversely proportional to time. So the ratio of times taken in both the cases will be 3:2. On ratio scale difference is 1 while actual difference is 2. so the time taken in first case is 6 hours and in second case it is 4 hours hence total distance covered is 10 × 6 = 60 km. he is taking 6 hours in first case and reaching there at 1 p.m. so must be had started at 7 a.m. To reach there at noontime taken is 5 hours and distance is 60 km. so speed should be 12 kmph.

Q10. SOL: 1
The first strip can be coloured in 4 ways 2nd in 3, 3rd in 3 and so on thus total no of ways = 4 *3 *3 *3 *3 *3 = 12 *81.

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