Problem 1 :
A fraction becomes 9/11, if 2 is added to both numerator and the denominator. If 3 be added to both the numerator and the denominator, the fraction becomes 5/6. Find the fraction.
Solution :
Let x/y be the required fraction
If 2 is added to both numerator and denominator the fraction becomes 9/11.
(x + 2)/(y+2) = 9/11
11(x + 2) = 9(y + 2)
11x + 22 = 9y + 18
11x – 9y = 18 – 22
11x – 9y = -4 ------(1)
If 3 is added to both the numerator and the denominator it becomes 5/6.
(x + 3)/(y+3) = 5/6
6(x + 3) = 5(y + 3)
6x + 18 = 5y + 15
6x – 5y = 15 - 18
6x – 5y = - 3 ------(2)
Solving (1) and (2), we get
x = 7
Substitute 7 for x in (1).
(1)-----> 11(7) – 9y = -4
77 – 9y = -4
-9y = -81
y = 9
Then,
x/y = 7/9
So, the required fraction is 7/9.
Problem 2 :
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Solution :
Let x be the age of Jacob and y be the age of his son.
5 years hence their ages will be
x + 5 and y + 5
x + 5 = 3(y + 5)
x + 5 = 3y + 15
x – 3y = -5 + 15
x – 3y = 10 ------(1)
5 years ago, their ages were
x – 5 and y – 5
x – 5 = 7(y – 5)
x – 5 = 7y – 35
x – 7y = 5 - 35
x – 7y = -30 ------(2)
(1) - (2) :
4y = 40
y = 10
Substitute 10 for y in (2).
(2)------> x - 7(10) = -30
x – 70 = -30
x = 40
Therefore,
age of Jacob's son = 10
Age of Jacob = 40
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