Quantitative Aptitude - Arithmetic Ability Questions

Here, s={H,T} and E={H}
P(E) = n(E)/n(S) = 1/2

In these type of fractions, the decimal moves left the number of zeroes in the divisor times. Herein the given question 18/1000, there are 3 zeros in 1000 (divisor). Hence, the quotient is 0.018.

The quotient of 18/1000 = 0.018.

In the question it is asked for 5% of 1500

5 x 1500/100 = 15 x 5 = 75.

Hence, 5% of 1,500 is equal to 75.

There is 1 way to correctly guess who comes in first, second, and third. There is only one set of first, second and third place winners. You must correctly guess these three people, and there is only one way to do so.

After day 1, A finishes 1/9 of the work.

After day 2, B finishes 1/7 more of the total work. (1/9) + (1/7) is finished.

After day 3, C finishes 1/5 more of total work. Total finished is 143/315.

So, after day 6, total work finished is 286/315.

Now remaining work =  29 /315

On day 7, A will work again 

Work will be completed on day 7 when A is working. He must finish 29/315 of total remaining work.

Since he takes 9 days to finish the total task, he will need 261/315 of the day. 

Total days required is 6 + (261/315) days.

There are 12 - 3 = 9 patients.They can be seen in 12P9 = 79833600 ways

Let
P's capital = p,
Q's capital = q and
R's capital = r.
Then

6p = 8q = 12r
=> 3p = 4q = 6r
=>q = 3p/4
r = 3p/6 = p/2
P : Q : R = p : 3p/4 : p/2
= 4 : 3 : 2
R's share = 4650 * (2/9) = 150*6 = Rs. 1033.33.