three consecutive numbers are such that when they are taken in increasing order and multiplied by 2 3 and 4 respectively they add up to 74 find the numbers
the ages of Rahul and Neha in the ratio 5 is to 7 4 years later the sum of their ages will be 56 years what are the present ages
Answers
Answer:
For question 1: The numbers are 7, 8 and 9
For question 2: Their current ages are 20 and 28
Step-by-step explanation:
Question 1:
Let the three consecutive numbers be n, n+1 and n+2, when taken in increasing order
If they are multiplied by 2, 3 and 4 respectively, the numbers become
2n, 3(n+1) and 4(n+2)
Now, since these three numbers add upto 74, we get
2n + 3(n+1) + 4(n+2) = 74
=> 2n + 3n + 3 + 4n + 8 = 74
=> 9n + 11 = 74
=> 9n = 63
=> n = 7
So, the consecutive numbers are 7, 8 and 9
Now, let us check the answer: if you multiply them by 2, 3 and 4 respectively, we get 14, 24 and 36
14 + 24 + 36 = 74
So, our answer is correct.
Question 2:
Let the ages of Rahul and Neha be R and N respectively.
So, R:N = 5:7
i.e, if R = 5x, then N = 7x
4 years later, their ages will be R+4 and N + 4. i.e, 5x + 4 and 7x + 4
Since 4 years later sum of their ages will be 56, we get
(R+4) + (N+4) = 56
i.e, (5x +4) + (7x+4) = 56
=> 12x + 8 = 56
=> 12x = 48
=> x = 4
=> R = 5x = 20 and N = 7x = 28
So, Rahul and Neha are 20 and 28 years old currently.