Question

1) the sum of three consecutive integers even is 3,2,1. find the integers.

2) the sum of the digits of a two digit number is 14. If the number formed by reversing the digits is less than the original number by 18. Find the number
3) the denominator of a rational number is less than the numerator by 5. If 5 is added to the numerator the new number becomes 11/6. Find the number
4) the ages of Ruby and reshma are in the ratio 5:7. Four years later their ages will be in the ratio 3:4. Find their ages. ​

Answer 1

3)The original rational number was 17/12.

4)The age of Ruby and Reshma are 20 and 28 years respectively.

Step-by-step explanation:

3)Let the numerator be x.

So denominator will be (x - 5)

If we add 5 to numberator then it will be (x + 5)

New number is (x + 5)/(x - 5)=11/6

Solve for X by cross multiplying

6(x + 5)=11(x - 5)

6x + 30=11x - 55

5x=85

x=17

So original rational number was 17/12.

4)The ages of Ruby and Reshma are in the ratio 5:7

So, let the present ages of Ruby and Reshma be 5x and 7x respectively.

Also, it is given that four years from now the ratio of their ages will be 3:4

So, the equation - 5x + 4 / 7x + 3 = 3/4

⇒4(5x+4)=3(7x+4)

⇒20x+16=21x+12

⇒21x−20x=16−12

⇒x=4

⇒5x=20 and 7x=28

The age of Ruby and Reshma are 20 and 28 years respectively.