MATHEMATICS

1. Two pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

A. 3 min                B. 2.5 min         C. 2 min         D. 1.5 min

Answer : Option D

Explanation :

Part filled by the first pipe in 1 minute = ½

Part filled by the second pipe in 1 minute = 1/6

Net part filled by pipe A and pipe B in 1 minute = 1/2+1/6=2/3

i.e, pipe A and B together can fill the tank in 3/2 minutes = 1.5 minutes

2. One pipe can fill a tank 6 times as fast as another pipe. If together the two pipes can fill the tank in 22 minutes, then the slower pipe alone will be able to fill the tank in:

A. 164 min           B. 154 min         C. 134 min              D. 144 min

Answer : Option B

Explanation :

Let the slower pipe alone can fill the tank in x minutes

Then the faster pipe can fill the tank in x/6 minutes

Part filled by the slower pipe in 1 minute = 1x

Part filled by the faster pipe in 1 minute = 6x

Part filled by both the pipes in 1 minute = 1x+6x

It is given that both the pipes together can fill the tank in 22 minutes⇒ Part filled by both the pipes in 1 minute = 1/22

1x+6x=1/22

7x=1/22

x=22×7=154

i.e.,the slower pipe alone fill the tank in 154 minutes

3. Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:

A. 18 hr       B. 6 hr    C. 24 hr          D. 12 hr

Answer : Option D

Explanation :

Part filled by pipe A in 1 minute = 1/8

Part filled by pipe B in 1 minute = 1/24

Part emptied by pipe C in 1 minute = 1/12

Net part filled by pipe A, pipe B and pipe C in 1 minute

= 1/8+1/24−1/12

=2/24

=1/12

i.e, the tank will be filled in 12minutes

4. Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 3 minutes, then how much more time will it take to fill the tank by tap B?

A. 6 min 15 sec     B. 5 min 45 sec       C. 5 min 15 sec           D. 6 min 30 sec

Answer : Option B

Explanation :

Part filled by pipe A in 1 minute = 1/8Part filled by pipe B in 1 minute = 1/14Part filled by pipe A and pipe B in 1 minute = 1/8+1/14=11/56

Pipe A and pipe B were open for 3 minutes

Part filled by pipe A and pipe B in 3 minutes = 3×11/56=33/56Remaining part = 1−33/56=23/56

Time taken by pipe B to fill this remaining part

 = (23/56)x14

=23×14/56

=23/4 minutes

=5.75mts

= 5 minutes 45 seconds

5. A water tank is two-fifth full. Pipe A can fill a tank in 12 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

A. 2.8 min            B. 4.2 min     C. 4.8 min    D. 5.6 min

Answer : Option C

Explanation :

Since pipe B is faster than pipe A, the tank will be emptied.

Part filled by pipe A in 1 minute = 1/12

Part emptied by pipe B in 1 minute = 1/6

Net part emptied by pipe A and pipe B in 1 minute = 1/6−1/12=1/12

Time taken to empty the tank = 12 min

Time taken to empty 2/5 of the tank = (2/5)×12=4.8 min

6. 13 buckets of water fill a tank when the capacity of each bucket is 51 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 17 litres?

A. 33      B. 29      C. 39       D. 42

Answer : Option C

Explanation :

Capacity of the tank = (13 × 51) litre

Number of buckets required of capacity of each bucket is 17 litre

 = 13×51/17

=13×3=39

7. Two pipes A and B can fill a tank in 9 hours and 3 hours respectively. If they are opened on alternate hours and if pipe A is opened first, how many hours, the tank shall be full?

A. 4 hr   B. 5 hr    C. 2 hr     D. 6 hr

Answer : Option B

Explanation :

Part filled by pipe A in 1 hour = 1/9

Part filled by pipe B in 1 hour = 1/3

Pipe A and B are opened alternatively.

Part filled in every 2 hour = 1/9+1/3=(1+3)/9=4/9

Part filled in 4 hour = 2×4/9=8/9

remaining part =1−8/9=1/9

Now it is pipe A's turn.

Time taken by pipe A to fill the remaining 1/9 part

=(1/9)x9

=1 hour

Total time taken = 4 hour + 1 hour = 5 hour

8. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. What is the cost price of a ball?

A. Rs. 43                     B. Rs. 60         C. Rs. 55                D. Rs. 34

Answer : Option B

Explanation :

Loss = (CP of 17 balls) - (SP of 17 balls)

 = (CP of 17 balls) - 720

Given that Loss = (CP of 5 balls)

=> (CP of 17 balls) - 720 = (CP of 5 balls)

=> (CP of 17 balls) - (CP of 5 balls) = 720

=> CP of 12 balls = 720

=> CP of 1 ball=720/12

=60

9. A man sells two houses at the rate of Rs.1.995 lakhs each. On one he gains 5% and on the other, he loses 5%. What is his gain or loss percent in the whole transaction?

A. 0.25%.             B. .3%         C. .4        D. .5%

Answer : Option A

Explanation :

If a person sells two items at the same price; one at a gain of x % and another at a

loss of x %, then the seller always incurs a loss expressed as

Loss%=(Common Loss and Gain%/10)/2=(x/10)/2

Loss%=(5/10)/2=(1/2)/2=(1/4)=.25

10. A shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight. What is his profit percentage?

A. 18%      B. 40%        C. 25%          D. 20%

Answer : Option C

Explanation :

If a trader professes to sell his goods at cost price, but uses false weights, then

Gain%=[Error/(True Value−Error)×100]%

So here profit percentage=[200/(1000−200)×100]%

=[200/800×100]%

=25%