Quantitative Aptitude - Arithmetic Ability Questions

x / y  = 0.04 / 1.5 = 4 / 150 = 2 / 75.

= > ( (y - x) / (y+x) ) = (1 - (x / y)) / ( 1 + ( x / y)) = (1 - 2/75) / (1 + 2/75) = 73/77...

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under: 

                                                      (1) (2) (3) (4) (5) (6) 

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.  

Number of ways of arranging the vowels = 3P3 = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions. 

Number of ways of these arrangements = 3P3 = 3! = 6. 

Total number of ways = (6 x 6) = 36.

B runs 35 m in 7 sec.

 B covers 200 m in (7/35*200) = 40 sec.

B's time over the course = 40 sec.

 A's time over the course (40 - 7) sec = 33 sec.

                       A   :   C    

Efficiency      5    :   3    

No of days   3x   :  5x     

Given that, 5x-6 =3x  => x = 3  

Number of days taken by A = 9  

Number of days taken by C = 15     

           B  :  C    

Days   2  :  3  

Therefore, Number of days taken by B = 10   

Work done by B and C in initial 2 days = 2110+115= 1/3  

Thus,  Rest work =2/3  

Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days

Less Men, means more Days {Indirect Proportion}

Let the number of days be x then,

27 : 36 :: 18 : x

[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]                                

=>27x = 36 * 18

=> x = 24

 So 24 days will be required to get work done by 27 men.

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.

 Number of 7 digit numbers = 7!3!×2! = 420

But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.

=6!3!×2! = 60

Hence the required number of 7 digits numbers = 420 - 60 = 360