## Probability, Time and Work, Percentage

1. The age of father 10 years ago was thrice the age of his son. Ten years hence, father′s age will be twice that of his son. What is the ratio of their present ages?

2. Praveen and Raja invested in a business. The profit earned was divided in the ratio 2 : 3. If Praveen invested Rs 40000, find the amount invested by Raja?

3.In a single throw of a die, what is the probability of getting a number greater than 4?

4. If Raja and Gopi can do a job in 10 days and 15 days independently, How many days would they take to complete the same job working simultaneously?

1. 7 : 3

2. Rs. 6000.

3. ( 1 / 3 ).

4. 6 days.

1. Explanation:

Let the age of the son before 10 years = x
Age of the father before 10 years = 3x
( 3x + 20 ) = 2 * ( x + 20 )
( 3x + 20 ) = 2x + 40
3x – 2x = 40 – 20
x = 20
Age of the son at present = x + 10
= 20 + 10
= 30
Age of the father at present = 3x + 10
= ( 3 * 20 ) + 10
= 60 + 10
= 70
Required ratio = 70 : 30
= 7 : 3

∴ The ratio of their present ages is 7 : 3.

2. Explanation:

Let the amount invested by Raja = q
40000 : q = 2 : 3
40000 / q = 2 / 3
q = 40000 * ( 3 / 2 )
q = 20000 * 3
q = 60000

∴ The amount invested by Raja is Rs. 6000.

3. Explanation:

S = { 1, 2, 3, 4, 5, 6 }
n ( S ) = 6
E = Event of getting a number greater than 4.
= { 5, 6 }
n ( E ) = 2
P ( E ) = n ( E ) / n ( S )
= 2 / 6
= 1 / 3

∴ The propability is ( 1 / 3 ).

4. Explanation:

If total work is x.
Raja rate of working = x / 10 per day.
Gopi rate of working = x / 15 per day.
Rate of work = ( x / 10 ) + ( x / 15 )
Working days = x / [ ( x / 10 ) + ( x / 15 ) ]
= ( 30x / 5x )
= 6 days

∴ They take 6 days to complete the same job.