SOLUTION: Four years ago the ratio between the ages of suresh and deena was 5:3 respectively .the ratio between their present ages is 11:7 repectively. What will be deena's age 3 years hence

Question 884690: Four years ago the ratio between the ages of suresh and deena was 5:3 respectively .the ratio between their present ages is 11:7 repectively. What will be deena's age 3 years hence?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe this depends on who is the older one.
i'll assume suresh is the older one.
let x = the age of suresh today.
let y = the age of deena today.
the ratio of their ages today is x/y = 11/7
the ratio of their ages 4 years ago is (x-4) / (y-4) = 5/3
multiply both sides of x/y = 11/7 by y to get:
x = 11y/7
multiply both sides of (x-4) / (y-4) = 5/3 by (y-4) to get:
(x-4) = 5(y-4)/3
simplify this equation to get:
(x-4) = (5y-20)/3
replace x with 11y/7 in this equation to get:
(11y/7 - 4) = (5y-20)/3
since 4/1 = 28/7, simplify the expression on the left to get:
(11y-28)/7 = (5y-20)/3
multiply both sides of this equation by 21 to get:
3(11y-28) = 7(5y-20)
simplify both sides of this equation to get:
33y - 84 = 35y - 140
subtract 33y from both sides of this equation and add 140 to both sides of this equation to get:
56 = 2y
divide both sides of this equation by 2 to get:
y = 28
y = the age of deena today which means that deena's age today is 28.
3 years from now, deena's age will be 31.
your answer is deena's age will be 31 in 3 years.

you can confirm the answer is correct by applying y = 28 to both equations.
your original equations are:
x/y = 11/7
(x-4)/(y-4) = 5/3

in the first equation, if y = 28, then the equation becomes:
x/28 = 11/7
multiply both sides of this equation by 28 to get:
x = (11*28)/7 which results in:
x = 44

replace x with 44 and y with 28 in the second equation to get:
(x-4) / (y-4) = 5/3 which becomes:
(44-4) / (28-4) = 5/3 which becomes:
40 / 24 = 5/3 which is true because if you multiply 5/3 by 8/8 you will get 40/24 which means that 40/24 and 5/3 are equivalent to each other.

replace x with 44 and y with 28 in the first equation to get:
x/y = 11/7 becomes:
44/28 = 11/7
if you multiply 11/7 by (4/4) you will get 44/28.
this confirms that the ratio of 44/28 is equivalent to 11/7.

your answer is good.
deena'a age in 3 years will be 31 because 28 + 3 = 31.

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