IBPS RRB 2016-17 - Quant Quiz-14

1. Find the number of ways of distributing 8 identical balls into 3 boxes so that no box is empty and each box being large enough to accommodate all balls ?

A. 24
B. 28
C. 36
D. 21
E. 18

Sol. (8-1)C(3-1) = 7C2 = 7*6/2*1 = 21.

2. A group consists of 4 couples  in which each of the 4 men have one wife each. In how many ways could they arranged in a straight line so that the men and women occupy alternate position ?

A. 576
B. 982
C. 1152
D. 1024
E. None of these

Sol. 4!*4! + 4!*4! = 576+576 = 1152.

3. A five digit number is formed with the digits 0,1,2,3 and 4 without repetition.Find the chance that the number is divisible by 2 ?

A. 1/2
B. 2/3
C. 1/3
D. 1/4
E. None of these

Sol. 5 digit number = 5! = 120
Divisible by 2 then the last digit should be 0, 2, 4
Then no. of cases with 0 as last digit = 4! = 24
     no. of cases with 2 as last digit = 18
     no. of cases with 4 as last digit = 18
Total cases = 24 + 18 + 18 = 60
P = 60/120 = 1/2.

4. From a group of 4 men and 3 women , 2 persons are selected at random. Find the probability that at least one woman is selected ?

A. 2/3
B. 3/5
C. 5/7
D. 1/3
E. 1/2

Sol. Total cases = 7c2 = 7!/5!*2! = 21
     Cases when no women is selectd = 4c2 = 4!/2!*2! = 6
     Cases when atleast 1 woman is selected = (21-6) = 15
     Probability = 15/21 = 5/7.

5. 16 persons are participated in a party. In how many different ways can they host the seat in a circular table, if the 2 particular persons are to be seated on either side of the host ?

A. 16! * 2
B. 14! * 2
C. 18! * 2
D. 14!
E. None of these

Sol. (16 – 2)! * 2 = 14! * 2.

6. A and B start a business with investments of Rs. 10000 and Rs. 9000 respectively. After 4 months, A takes out 1/2 of his capital. After 2 more months, B takes out 1/3 of his capital while C joins them with a capital of Rs. 14000. At the end of a year, they earn a profit of Rs. 10160. Find the share of each member in the profit?

A. Rs A – Rs. 3300, B – Rs. 3500, C – Rs. 3360
B. Rs A – Rs. 3200, B – Rs. 3600, C – Rs. 3360
C. Rs A – Rs. 3200, B – Rs. 3700, C – Rs. 3260
D. Rs A – Rs. 3200, B – Rs. 3500, C – Rs. 3460
E. None of these 

Sol. A : B : C = (10,000 x 4 + 5000 x 8) : (9000 x 6 + 6000 x 6) : (14000 x 6)
= 80000 : 90000 : 84000 = 40 : 45 : 42
A’s share = Rs. 10160 x 40/127 = Rs. 3200;
B’s share = Rs. 10160 x 45/127 = Rs. 3600;
C’s share = Rs. 10160 x 42/127 = Rs. 3360.

7. 1, 4, 19, 54, 117, _

A. 194
B. 256
C. 216
D. 200
E. None of these

Sol. 1 + 1*3 = 4
     4 + 3*5 = 19
    19 + 5*7 = 54
    54 + 7*9 = 117
   117 + 911 = 216

8. Prachi started a business investing Rs. 50,000 in 2015, In 2016, she invested an additional amount of Rs. 20,000 and Arsh joined him with an amount of Rs. 70,000. In 2017, Prachi invested another additional amount of Rs. 20,000 and Heena joined them with an amount of Rs. 70,000. What will be Arsh’s share in the profit of Rs. 300,000 earned at the end of 3 years from the start of the business in 2015 ?

A)Rs Rs. 250,000.
B)Rs Rs. 120,000.
C)Rs Rs. 100,000.
D)Rs Rs. 150,000.
E)None of these

Sol. Prachi : Arsh : Heena
= (50000 x 12 + 70000 x 12 + 90000 x 12) : (70000 x 24) : (70000 x 12)
= 2520000 : 1680000 : 840000 = 3 : 2 : 1
Arsh’s share = Rs.300,000 x 2/6 = Rs. 100,000.

9. The ratio of the monthly salaries of A and B is in the ratio 15 : 16 and that of B and C is in the ratio 17 : 18. Find the monthly income of C if the total of their monthly salary is Rs 1,87,450. 

A. Rs 66,240
B. Rs 72,100
C. Rs 62,200
D. Rs 65,800
E. Rs 60,300

Sol. A/B = 15/16 and B/C = 17*18
So A : B : C = 15*17 : 16*17 : 16*18
= 255 : 272 : 288
So C’s salary = [288/(255+272+288)] * 1,87,450

10. X takes 6 days less than Y to finish the work individually. If X and Y working together complete the work in 4 days, then how many days are required by Y to complete the work alone ?

A. 7 days
B. 10days
C. 5 days
D. 12days
E.None of these

Sol. Lets assume Y takes = a days
Then X will take = (a-6) days

Now given, 1/a + 1/(a-6) = 1/4
Solving, we get,
a = 12 days.

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