1 . 
how many numbers between 300 and 800 can be by using digits 2, 4, 5, 6 and 0 ?


Answer & Explanation
Answer : Option
A


Explanation : 

∴ Reqd . numbers = 3 x ^{4}P_{2} = 3 x 12 = 36






2 . 
If two dice are thrown simultaneously, what is the probability that the sum of the numbers appeared is less than seven ?


Answer & Explanation
Answer : Option
B


Explanation : 

Sum of the numbers can be 2, 3, 4, 5, and 6
n(E) = 15, n (S) = 36 ∴ P (E) = 15/36 = 5/12






3 . 
The simple interest on a sum of money will be Rs. 2940 after 12 years. If the principal is increased five times after six years, what will be the total interest after 12 years ?


Answer & Explanation
Answer : Option
A


Explanation : 

Interest rate r = (2940 x 100/P x 12)%
= (24500/P)%
SI in first six years = P x 6 x 24500/P x 100 = 1470
SI in next six years = SP x 6 x 24500/P x 100 = 7350
∴ Total SI = 7350 + 1470 = 8820






4 . 
On a certain sum, the compound interest accrued in the first two years is Rs. 5520 and that in the first three years is Rs. 9576. What is the rate of interest ?


Answer & Explanation
Answer : Option
D


Explanation : 

CI = P[(x)1  1] where x = 1 + r/100
∴ P (x^{2}  1) = 5520 ...... (1)
P(x^{3}  1) = 9576 ...........(2)
Dividing eqn II by eqn I,
(x2 + x + 1) (x  1)/(x + 1) (x  1) = 9576/5520 = 399/230
= 230x^{2}  169x  169 = 0
= 230x^{2}  299x + 130x  169 = 0
= 23x (10x  13) + 13 (10x  13) = 0
∴ x = 13/10 and x = 13/23 (discardve)
1 + r/100 = 13/10 ∴ r = 30%






5 . 
Two numbers A and B are 20% and 45% more than a third number C, respectively. What percentage is the first number of the second number ?


Answer & Explanation
Answer : Option
D


Explanation : 

Let the third number be 100. So the first number is 100 + 100 x 20/100 = 120 and the second number is 145.
∴ Reqd answer = 120/145 x 100 = 82.758






6 . 
A shopkeepe, bought a cycle at 40% discount on its original price He sold it at a price 50% higher than in the original price What percentage profit did he make ?


Answer & Explanation
Answer : Option
D


Explanation : 

Let the original price of cycle be Rs. 100
∴ cost = 100  100 x 40/100 = 60
SP = 100 + 100 x 50/100 = 150
∴ Gain % = 15060/60 x 100 = 90 x 100/60 = 150%






7 . 
Two persons A and B can finish a piece of work in 60 days, while A, B, and C can finish the same work in 40 days. How many days will C alone take to finish the work ?


Answer & Explanation
Answer : Option
D


Explanation : 

Work doen by A and B together in one day = 1/60
Work done by A, B and C together in one day = 1/40
Work done by C in one day = 1/40  1/60 = 32/120 = 1/120
∴ C will take 120 days to finish the work.






8 . 
Two pipes A and B can fill a tank in 80 minutes and 60 minutes respectively. There is also an outlet C. If all the three pipes are opened together, the tank takes 40 minutes to fill completely. How much time will C take to empty the full tank ? (Answer in minutes)


Answer & Explanation
Answer : Option
D


Explanation : 

Work donee by C in one min
= 1/80 + 1/60  1/40 = 3+46/240 = 1/240
So, C will take 240 min to empty the tank.






9 . 
A train passes a pole in eight seconds and a platform in 23 seconds. If the length of the platform is 300 metres, what is the length of the train ?


Answer & Explanation
Answer : Option
C


Explanation : 

Let the length of the train be x.
∴ Speed of the train = x/8
Also,speed = x + 300/23
∴ x/8 = x + 300/23 ∴ 23x = 8x + 2400
or, 15x = 2400 ∴ x = 160 metres






10 . 
In a stream running at 3kmph. a boat goes 42 km upstream and comes back to the starting point in 306 minutes. What is the speed ol the boat in still water ?9


Answer & Explanation
Answer : Option
C


Explanation : 

Let the speed of the boat in still water be x kmph.
∴ 42/x + 3 + 42/x  3 = 306/60 = 51/10
or, [x3+x+3/x29] = 51/10 ∴ 84x/x29 = 51/10
or, 51x^{2}  840x  459 = 0
or, 17x^{2}  280x  153 = 0
or, 17x^{2}  289x + 9x  153 = 0
or, 17x(x  17) + 9 (x  17) = 0
or, (17x + 9) (x  17) = 0 ∴ x = 17, 9/17
Discarding ve, x = 17 kmh^{1}






