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Q1.In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.

a)10.5 minutes
b) 11.5 minutes
c) 12.5 minutes
d) 13.5 minutes
e) None of these

Q2. Three pipes A, B and C is attached to a cistern. A can fill it in 20 minutes and B can fill it in 30 minutes. C is a waste pipe.  After opening both the pipes A and B, Riya leaves the cistern to fill and returns when the cistern is supposed to be filled. But she found that waste pipe C had been left open, she closes it and now the cistern takes 5 minutes more to fill. In how much time the pipe C can empty the full cistern?

a) 26.8 minutes
b) 25.8 minutes
c) 27.8 minutes
d) 28.8 minutes
e) None of these

Q3. A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?

a) 15 minutes
b) 25 minutes
c) 35 minutes
d) 45 minutes
e) None of these

Q4. Smallest side of a right angled triangle is 6 cm less than the side of a square of perimeter 60 cm. Second largest side of the right angled triangle is 4 cm less than the length of rectangle of area 80 sq. cm and breadth 5 cm. What is the largest side of the right angled triangle?

a) 10cm
b) 9cm
c) 12cm
d) 15cm
e) None of these

Q5. A cylindrical tub of radius 10 cm contains water up to a depth of 25cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 5cm. What is the radius of the iron ball(approximate)?

a) 19
b) 15
c) 14
d) 17
e) None of these

Q6. When priya travels from home to office with a speed of 40km/hr she reaches her office late by 20 minutes and when she travels with 60km/hr, she reaches 10 minutes early. Find the distance between her office and home.

a) 50 km
b) 60 km
c) 65 km
d) 70 km
e) None

Q7. M start a business with Rs.26000 after 3 months N joined with Rs.16000. After some more months K joined with Rs.25000. At the end of the year they earned a total profit of Rs. 17000 and K gets Rs.4208 as his share. After how many months K joined the business after N?

a) 3
b) 4
c) 5
d) 2
e) None of these

Q8.A sum of money invested for 7years in Scheme 1 which offers SI at a rate of 8% pa. The amount received from Scheme 1 after 7 years invested for 2 years in Scheme 2 which offers CI rate of 10% pa. If the interest received from Scheme B was Rs.1638. What was the sum invested in Scheme 1?

a) Rs.7500
b) Rs.5000
c) Rs.8200
d) Rs.9000
e) None of these

Q9. From a deck of 52 cards, a card is selected and without replacing the card a new card is selected. Find out the probability that the first card is an ace and second card is a king?

a) 4/52*3/51
b) 4/51*3/52
c) 4/52*4/51
d) 3/52*3/51
e) None

Q10. A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?

a) 35/256
b) 33/220
c) 63/253
d) 43/190
e) 59/253

Solution:

Q1. SOL:   D

More the diameter more will be the water flowing through it and less will be the time taken.
Means bigger pipe will take less time to fill the tank
So, for 1 cm time, (1^2)/(3^2) = 21/t, we get t = 189
For 2 cm time, (2^2)/(3^2) = 21/t. We get t = 189/4
So total time = 1/21 + 1/189 + 4/189 = 2/27
So total time = 13.5 minutes

Q2. SOL:   D

The tank supposed to be filled in (30*20)/50 = 12 minutes
so, (1/20 + 1/30)*12 – 12/C + (1/20 + 1/30)*5 = 1 (A and B work for 12 minutes and also C work for 12 minutes and then A and B takes 5 more minutes to fill the tank)
solve for C, we will get C = 144/5 = 28.8

Q3.  SOL:   D

Time taken by a deer to complete one round = 9 minutes
Time taken by a rabbit to complete one round = 5 minutes
They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.

Q4. SOL:   D

Side of 1st square = 60/4 = 15 cm.
Smallest side of right angled triangle= 15 −6 = 9 cm.
Length of 2nd rectangle = 80/5 = 16 cm.
Second largest side of the 1strectangle = 16−4 = 12 cm.
Largest side = hypotenuse=√9^2+12^2=15cm

Q5. SOL:   C

Volume of the ball = volume of the raised water
4*22*r3/3*7 = 22*100*5
r= 11000*3*7/88 = 2625
r = 13.79 or 14

Q6. SOL:   B

D = 40(t+20/60) and D = 60(t-10/60)
solve these two equation and get D.

Q7. SOL:   A

26000*12 : 16000*9 : 25000*6
312:144:150 = 156 : 72 : 75
K’s share = 17000* 75/303 = 4208
9-6 = 3

Q8. SOL:   B

SI =>Amount = x*8*7/100 + x = 56x+100x/100 = 156x/100 = 39x/25
CI=> 39x/25[(1+10/100)2 – 1] 1638 = 39x/25[121/100 – 1] = 39x/100[21/100] X = 1638*100*25/21*39 = 5000

Q.9 SOL:   C

4/52*4/51

Q10. SOL:   C

From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2*16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253