Q1.Bag A contains 7 Red Balls, ‘X’ Green Balls, and 5 Yellow Balls. The probability to pick Green Ball at random is 2/5. Another Bag B contains ‘X-3’ Red Balls, ‘X-4’ Yellow Balls and 6 Green Balls. If two balls are picked one after the other from Bag B at random then what is the probability for the Balls to be Red?

1. 1/21
2. 2/21
3. 3/21
4. 4/21
5. Cannot be determined

Q2. A boat takes 30 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 2 kmph and the speed of the boat in still water is 15 kmph, what is the distance between A and B?

1. 342km
2. 356km
3. 316km
4. 308km
5. None of these

Q3. Working together Bala and Chitra take 50% more number of days than Angel, Bala and Chitra together take and Angel and Bala working together, take 8/3 more number of days than Angel, Bala and Chitra take together. If Angel, Bala and Chitra all have worked together till the completion of the work and Bala has received Rs.120 out of total earnings of Rs. 480 then in how many days did Angel, Bala and Chitra together complete the whole work?

1. 2 days
2. 4 days
3. 6 days
4. 8 days
5. 5 days

Q4. A father left a will of Rs.5 lakhs between his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.5 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?

1.Rs.2,04,797
2.Rs.3,05,890
3.Rs.1,90,00
4.Rs.4,00,700
5.Rs.2,46,870

Q5. Two Vans start from a place with a speed of 50 kmph at an interval of 12 minutes. What is the speed of a car coming from the opposite direction towards the place if the car meets the vans at an interval of 10 minutes?

1. 13 kmph
2. 10 kmph
3. 14 kmph
4. 16 kmph
5. None of these

Q6. A sum of rupees 4420 is to be divided between rakesh and prakash in such a way that after 5 years and 7 years respectively the amount they get is equal. The rate of interest is 10 percent. Find the share of rakesh and Prakash

1. 2000, 2420
2. 2420, 2000
3. 2480, 2420
4. 2210, 2210
5. None of these

Q7. Suppose children like three types of chocolates Perk, Munch, and 5Star. If they are asked to choose to pick chocolate they have their own preference, one-sixth of children population preference is Perk>Munch>5star. One-sixth of children population preference is Munch>5star>Perk. Similarly remaining four-sixths children preferences follows as per above combinations. If you met a random child and give him chance to pick a chocolate between Munch and Perk. He picked Munch. Now you offer Munch and 5star, what is the probability that he chooses again Munch?

1. 1/6
2. 1/2
3. 2/3
4. 3/4
5. None

Q8.A bag contains 100 tickets, numbered from 1 to 100. If three tickets are picked at random and with replacement, what is the probability that sum of three numbers on the tickets will even number?

1. 1/2
2. 3/4
3. 1/8
4. 3/8
5. None

Q9. Two persons A and B start from the opposite ends of a 450 km straight track and run to and from between the two ends. The speed of the first person is 25 m/s and the speed of other is 35 m/s. They continue their motion for 10 hours. How many times did they pass each other?

1. 1
2. 4
3. 3
4. 2

5. 3

Q10. A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is

1. 10kmph
2. 4kmph
3. 6kmph
4. 8kmph
5. None of these

Solution:

Q1.SOL:   2

X/(7+X+5) =2/5
X =8
Bag B = 5 R, 4 Y , 6 G
Probability = 5/15*4/14 = 2/21

Q2. SOL:   4

velocity of the stream = 2 kmph
Speed of the boat in still water is 15 kmph
Speed downstream = (15+2) = 17 kmph
Speed upstream = (15-2) = 13 kmph
Let the distance between A and B be x km
x/17+(x/2)/13=30
x/17+x/26=30
43x/442=30
x=30*442/43 = 308.37 = 308km
distance between A and B = 308 km

Q3.SOL:   5

The days ratio of (Angel + Bala + Chitra) : (Bala + Chitra) = X:3X/2 = 2X:3x;
Efficiency ratio = 3X:2X
Efficiency of Angel = x.
(480/3X) = Rs.160
Amount received by Bala = Rs.120 &Chitra = 200
160:120:200 =4:3:5
1/4:1/3:1/5= 15:20:12;
(1/15+1/12+1/20)*Y = 1
Y = 5 days

Q4. SOL:   1

Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (5,00,000 – x).
The elder daughter’s money earns interest for (21 – 15) = 6 years @ 10% p.a simple interest
The younger daughter’s money earns interest for (21 – 10) = 11 years @ 10% p.a simple interest.
As the sum of money that each of the daughters get when they are 21 is the same,
x + (6*10*x/100)= (5,00,000 – x) +(11*10*[5,00,000-x]/100)
100x+60x = (5,00,000-x)+(55,000,000-110x)
160x =55,500,000-111x
271x = 55,500,000
X = 2,04,797

Q5. SOL:   2

50*12/60 = 10/60 * (50+x)
600 = 500 + 10x
x = 10 kmph

Q6. SOL:   2

Let the share of rakesh and prakash be R and P
R*(1+10/100)5 = (4420 – R)*(1+10/100)7
We get R = 2420, so P = 2000

Q7.  SOL:   3

Possible preferences
P>M>5
M>5>P
P>5>M
M>P>5
5>P>M
5>M>P
Child picks Munch over Perk P(M5P), P(MP5) or P(5MP)
Then child prefers Munch over 5star P(M5P) P(MP5)
Probability = (1/6+1/6)/(1/6+1/6+1/6) =2/3

Q8. SOL:   1

P(odd) = P(even) = 1/2
Sum of three numbers to be even cases
Even+ even+ even = 1/2*1/2*1/2
Even+ odd+ odd = 1/2*1/2*1/2
Odd+ odd + even = 1/2*1/2*1/2
Odd+ even + odd = 1/2*1/2*1/2
Probability = 1/8+1/8+1/8+1/8 = ½

Q.9 SOL:   4

First person speed = 25 m/s * 18/5 = 90 kmph
Second person speed = 35 m/s * 18/5 = 126 kmph
First person covers 90 * 10 = 900km
900/450 = 2

Q10. SOL:   1

speed of the boat in still water = x kmph
speed of the current = y kmph
upstream speed = (x – y) kmph
downstream speed = (x + y)kmph
24/(x-y) + 28/(x+y) = 6
30/(x-y) + 21(x+y) = 13/2
X = 10kmph

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