1. two numbers are in ratio 13:10.if they differ by 99.what are the numbers?
2. The sum of two numbers is 8 and their difference is 4.find numbers?
3. I am three times as old as my son.Five years later,i will be only 2 1/2 times older thanhim.how old are we now?

1. Let the two numbers be 13x and 10x

= 13x - 10x = 99

= 3x = 99

= x = 33

SO the numbers

(13x) = 429

(10x) = 330

2. Let the number be x and y

Then according to question

x+y = 8 and x-y = 4

now adding both

x + y + x - y = 8 + 4

2x = 12

x = 6

Now according to question

x + y = 8

6 + y = 8

y = 2

So the numbers are 6 and 2 (ans)

Let the age of son be X

Then the age of father = 3X

Now,

their age after 5 years

Age of son = X+5

Age of father = 3X+5

But according to question

Age of father is equal to 5/2 times the son

So,

Age of son = Age of father

= 5/2(X+5) = 3X+5

= 5/2X + 5/2*5 = 3X+5

= 5/2X + 25/2 = 3X+5

= 5/2X - 3X = 5 - 25/2

= (5x - 6x)/2 = (10 -25)/2

= -x/2 = -15/2

= -2x = -30

= X = -30/-2

= 15

Then the ,

Present age of son = 15 years

Present age father = 45years

Proof

Age of son after 5 years = X +5

= 15 + 5

= 20years

Age of father after 5 years = 3x+5

= 45+5

= 50

Now we will see that according to question age of father

Age of father is equal to 5/2 times the son = 20*5/2

= 50years

PROOVED