11 years ago, Ali's age was 5 times of Waleed's
age. After 7 years, Ali's age will be 2 times of
Waleed's age. Find their ages.
Answers
The solution is done below :
Let,
The present age of Ali be A.
Then,
Ali's age before 11 years was = (A - 11)
And,
Ali's age after 7 years will be = (A + 7)
Let's say that, Waleed's age is W.
Therefore, to solve this problem we have to take Waleed's age before 11 years and after 7 years also.
So, according to question, the equations will be,
A - 11 = 5 (W - 11)
=> A - 11 = 5W - 55
=> A - 11 + 55 = 5W
=> A + 44 = 5W ----- eq. (i)
A + 7 = 2 (W + 7)
=> A + 7 = 2W + 14
=> A - 7 = 2W ------- eq. (ii)
Sloving this two equations, we get,
A + 44 - (A - 7) = 5W - 2W
A + 44 - A + 7 = 3W
51 = 3W
W = 17
Therefore,
Waleed's age is 17 years.
Putting the value of W in equation (i), we get,
A + 44 = 5W
A + 44 = 5 x 17
A + 44 = 85
A = 85 - 44
A = 41
Hence,
Ali's age is 41 years.
Present age of Ali=41 years,Present age of Waleed=17 years
Step-by-step explanation:
Let us assume that,
Present age of Ali be x years.
Then,
Ali's age 11 years ago = (x - 11)
Ali's age after 7 years = (x+ 7)
Now,Let Waleed's Present age is y year
Waleed's age 11 years ago=y-11 years
Waleed's age after 7 years =y+11years
Now, according to question,
x - 11 = 5 (y - 11)
=> x- 11 = 5y - 55
=> x - 11 + 55 = 5y
=> x + 44 = 5y ----- eq. (i)
Also,
x + 7 = 2 (y + 7)
=> x + 7 = 2y + 14
=> x - 7 = 2y ------- eq. (ii)
On solving these two equations, we get,
x + 44 - (x - 7) = 5y - 2y
x + 44 - x + 7 = 3y
51 = 3y
y = 17
⇒Waleed's present age is 17 years.
Put the value of y in equation (i), we get,
⇒x + 44 = 5y
⇒x + 44 = 5 x 17
⇒x+ 44 = 85
⇒x = 85 - 44
⇒x = 41
Hence,
Ali's present age is 41 years.