Quantitative Aptitude - Arithmetic Ability Questions

1 million distinct 3 digit initials are needed.

Let the number of required alphabets in the language be ‘n’.

Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.

Note distinct initials is different from initials where the digits are different.

For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.

This n3 different initials = 1 million 

i.e. n3=106  (1 million = 106)

  => n = 102 = 100

Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.

One-quarter of one-seventh = 1/4 x 1/7
= 1/28
Now, 1/28 of a land costs = Rs. 30,000
Thus, 8/35 of the land will cost = 30,000 x 28 x 4/15
= Rs. 2,24,000.

Total coins 30

In that,

1 rupee coins 20

50 paise coins 10

Probability of total 1 rupee coins =  20C11

Probability that 11 coins are picked = 30C11

Required probability of a coin now picked from the box is 1 rupee = 20C11/30C11 = 2/3.

Here,P(A)=4/9=p/(p+q)

P(odd against event A)=q/p=5/4

Number of shares = 14400120=120.

Face value = Rs.(100 x 120) = Rs.12000.

Annual income = Rs (5/100*12000) = Rs. 600

Let the rate be R% p.a.

I  gives, P = Rs. 8000 and T = 4 years.

II gives, S.I = Rs. (8800 - 8000) = Rs. 800.

R = [100 x S.I] / [p x t ]= (100 x 800)/(8000 x 4) = 2 ½ % p.a

Thus, I and II both are needed to get the answer.

(16M + 12W) x 20 = 18W x 40

=> 2M = 3W

Then,
Convert all men into women

12M + 27W = 27 + 12 x 3/2W = 45W

Let number of days required be 'D'

=> 18 x 40 = 45 x D

=> D = 16 days.

B runs around the track in 10 min.

 i.e ,    Speed of B = 10 min per round

 Therefore,  A beats B by 1 round

  Time taken  by A to complete 4 rounds 

  = Time taken by B to complete 3 rounds  

 = 30 min 

Therefore, A's speed = 30/4 min per round = 7.5 min per round

 Hence, if the race is only of one round A's time over the course = 7 min 30 sec