Quantitative Aptitude - Arithmetic Ability Questions

Number of persons * days = work  

20 * 7 = 140 man- days 

Now,  x * 28  = 140 men- days

=> x =5         

Therefore in second case the required number of person is 5.

Second method:

Since work is constant, therefore  M1 x D1= M2 x D2

20 x 7 = M2 x 28

=> M2 = 5 

Speed = 108 km/hr
enter a tunnel,, means that the train covers a distance equal to its own length
so (108 x 5/18) = x/4 where x= length of train
hence x = 120 mtrs
to pass completely train has to travel a distance = (x + tunnel length) that is 1120 mtrs.
so (1120/t) = (108x5/18)
t = 37.33 sec

2(l+b)/b = 5/1 

=> 2l + 2b = 5b  

=> 3b = 2l  

=> b =(2/3) x l

 Then, Area = 216 sq.cm 

l x b = 216  

=> l x [(2/3)x l] =216  

=> l x l = 324 

=> l = 18 cm.

There are 13 spades,we must include 2: 13C2

There are 13 diamonds,we must include 3: 13C3

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts : 26C2

Therefore,13C2*13C3*26C2 = 7250100

Let the price of 1 litre of diesel be Rs.x and let Karthik initially buy 'y' litres of diesel.
Therefore, he would have spent Rs. xy on diesel.

When the price of diesel increases by 25%, the new price per litre of diesel is 1.25x.

Karthik intends to increase the amount he spends on diesel by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy

Let the new quantity of diesel that he can get be 'q'.
Then, 1.25x x q = 1.15xy
Or q = (1.15/1.25)y = 0.92y.

As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.

Or a reduction of 8%.

Given K=4L 

-->K+L = 4L+L = 5L

These 5L people can complete the work in 24 days, which means L alone can do the work in (24 x 5)=120 days.

Hence, K alone can do the work in 120/4= 30 days.

Let the Efficiency of pavan be E(P)

Let the Efficiency of sravan be E(S)

Here Work W = LCM(25,20) = 100

Now, E(P+2S) = 100/25 = 4 ....(1)

E(2P+S) = 100/20 = 5 ....(2)

Hence, from (1) & (2) we get

E(S) = 1

=> Number of days Savan alone work to complete the work  = 100/1 = 100 days.

S = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }

=> n(S) = 8

E = { HHH, HHT, HTH, THH }

=> n(E) = 4

P(E) = 4/8 = 1/2