Quantitative Aptitude - Arithmetic Ability Questions

Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event

∴A, B, C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

 PA=12, PB=23, PC= 34

∴ P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  = PA∩B∩C 

                  = PAPBPC         ∵ A, B, C are Independent                       

                  =  12×23×34  

                  = 14  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                = 1-14= 3/4

Let the number be x.

Then, ideally he should have multiplied by  x by 5/3. Hence Correct result was x * (5/3)= 5x/3. 

By mistake he multiplied x by 3/5 . Hence the result with error  = 3x/5 

Then, error = (5x/3 - 3x/5) = 16x/15 

Error %  = (error/True vaue) * 100 = [(16/15) * x/(5/3) * x] * 100 = 64 %

Let S.P. of 45 lemons be Rs. x.

Then, 80 : 40 = 120 : x or   x = 40×12080= 60

For Rs.60, lemons sold = 45

For Rs.24, lemons sold  =4560×24= 18.

Let S be the sample space

Then n(S) = no of ways of drawing 2 balls out of (6+4) =10C2 10 =10*92*1 =45

Let E = event of getting both balls of same colour

Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)

                =6C2+4C2 = 6*52*1+4*32*1= 15+6 = 21

Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15

Purchase price = Rs.87481-101003 = Rs. [8748 * (10/9) * (10/9 )* (10/9)] = Rs.12000

Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours. 

24 hours 10 min. of this clock = 24 hours of the correct clock. 

1456 hrs of this clock = 24 hours of the correct clock. 

29 hours of this clock = 24*6145*29 hrs of the correct clock 

= 28 hrs 48 min of the correct clock. 

Therefore, the correct time is 28 hrs 48 min. after 8 a.m. 

This is 48 min. past 12.

Let the C.P be Rs.100 and S.P be Rs.x, Then
The profit is (x-100)
Now the S.P is doubled, then the new S.P is 2x
New profit is (2x-100)
Now as per the given condition;
=> 3(x-100) = 2x-100
By solving, we get
x = 200
Then the Profit percent = (200-100)/100 = 100
Hence the profit percentage is 100%