Aptitude

Now, 16 women can complete the work in 12 days. So, 32 women will do it in 6 days. ((12 * 16) / 32 = 6 days).  It is the correct answer.

(A + B) can do the work in (4 * 8) / (4 + 8) = 32/12 = 8/3 days

Therefore, C takes 8/3 days to complete the work.
So, (B + C) takes ((8/3) * 8)/((8/3) + 8) = 64/32 = 2 days.
It is the correct answer.

Part of the capacity of the cistern emptied by leakage in 1 hour = (1/8 - 1/9) = (9 - 8)/(8 * 9) = 1/72

Therefore, the leakage will take 72 hours to empty the cistern. This is answer correct.

Man's rate while going downstream = (8 + 1.6) = 9.6 km/hr

Man's rate going upstream = (8 - 1.6) = 6.4 km/hr

Let the required distance be x km.

Then, (x/9.6) + (x/6.4) = 1

6.4x + 9.6x = 6.4 * 9.6

16x = 6.4 * 9.6

x = (6.4 * 9.6)/16

x = 6.4 * 0.6

x = 3.84 km

It is the correct answer.

If the speed of horse is x km/hr, then the speed of the train is 3x km/hr (speed of train is 3 times the speed of the horse)

Speed of the train = 1^1/2 of the speed of the ship = 3/2 of ship's speed,
i.e. speed of ship = 3x/(3/2) = 2x km/hr

Total time taken is 15 hrs and 30 min = 15 + 30/60 = 15 + 1/2 = 31/2 hrs.
Therefore,
(140/2x) + (600/3x) + (40/x) = (31/2)

70/x + 200/x + 40/x = 31/2

310/x = 31/2

x = 20
Speed of the train is 3x = 3 * 20 = 60 km / hr.
 It is the correct answer.

If A rides for X hrs before he is overtaken by B, then B rides for (X - 1.5) hrs.
Therefore, 10X = 12(X - 1.5)

12 * 1.5 = 12X - 10X

12 * 1.5 = 2X

6 * 1.5 = X

X = 9.0

So, A will have ridden 10 * 9.0 = 90 km.

It is the correct answer.

When two dice are thrown then there are 6 * 6 exhaustive cases. Therefore, n = 36.

Let A denote the event total score of 8 when 2 dice are thrown. Then A = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

Thus, there are 5 favourable cases.

Therefore, m = 5

By definition P(A) = m/n = 5/36.

It is the correct answer.

Difference between time = 18 - 10 = 8 min

= 8/60 hr

= 2/15 hr

Required distance = ((Speed1 * Speed2)/(Speed1 - Speed2)) * difference of time

Required distance = ((15 * 20)/(20 - 15)) * (2/15)

                          = (15 * 20 * 2)/(5 * 15) = 8 km

It is the correct answer.

Out of four boys, Aman has to invite exactly three boys. This can be done in ⁴C₃ ways.

Out of three girls, she can invite one or two or three girls or none of them in 2³ i.e 8 ways.

So, total number of ways are ⁴C₃ * 8 = 32 ways.
It is the correct answer.

or 1 man working for 1 hr cuts 70/(50 * 8) trees.

Thus, 40 men working for 12 hrs will cut (70 * 40 * 12)/(50 * 8) trees  = 84 trees.

It is the correct answer.

There are 4 cases only, either all 4 boxes have a red ball, or 3 have a red ball or 2 have a red ball or 1 has a red ball.
So, as they are numbered consecutively, total number of ways when only 1 box has red ball
= 4 as it can be in any of the four boxes.
Similarly, for 2 boxes having red balls, total number of ways = 3,
For 3 boxes having red balls, the total number of ways = 2
and for 4 boxes having red boxes, the total number of ways = 1.

Therefore, total number of ways = 4 + 3 + 2 + 1 = 10.

It is the correct answer.

A did 1/3th of the workin 6 days.
B completed 1/4th of the work in 6 days.
Work completed by C in 6 days = 1 - (1/3) + (1/4) = 5/12th of the work
Since A, B and C did the work in 6 days 1/3th, 1/4th, 5/12th of the work, respectively.
A's share = Rs 51 * (1 / 3) = Rs. 17
B's share = Rs 51 * (1 / 4) = Rs. 12.75
C's share = Rs 51 * (5 / 12) = Rs. 21.25.
So B's share is Rs 12.75.
It is the correct answer.

Therefore, (t/30) + ((t - 1)/40) + ((t - 2)/60) + ((t - 3)/120) = 1                  4t + 3(t - 1) + 2(t - 2) + t - 3 = 120                                           t = 13 hours Therefore, the reservoir will be filled at 7 pm.  It is the correct answer.

Let the length of each train be x metres.

Then, the total distance covered by the faster train in 54 sec = (x + x) = 2x m

Relative speed = (58 - 48) km/h

                      = 10 km/h
                   
                      = (10 * 5)/18 m/s (since both trains are moving in the same direction)

Hence, time = distance/speed

54 = 2x/(50/18)

54 = (2x * 18)/50

x = (54 * 50)/(18 * 2)

x = 3 * 25 x = 75 m

It is the correct answer.