the present age of A and B are in the ratio of 8:7, 27 years agotheir age was in the ratio of 5:4 Find the age of elder one?
Answers
Answer:
27 years ago their age was in the ratio 5:4 . Clearly, here A is elder than B . Hence, The present age of elder one is 72 years .
Step-by-step explanation:
Given :-
The present age of A and B are in the ratio of 8:7, 27 years ago their age was in the ratio of 5:4.
To find:-
Find the age of elder one?
Solution:-
Given that
The ratio of the present ages of A and B = 8:7
Let they be 8X and 7X
The present age of A = 8X years
The present age of B = 7X years
27 years ago the age of A = (8X-27) years
27 years ago the age of B = (7X-27) years
The ratio of the ages of A and B ,27 years ago
= (8X-27) : (7X-27)
According to the given problem
27 years ago their age was in the ratio of 5:4.
=> (8X-27) : (7X-27) = 5:4
=> (8X-27) / (7X-27) = 5 / 4
On applying cross multiplication then
=> 5(7X-27) = 4(8X-27)
=> (5×7X)-(5×27) = (4×8X)-(4×27)
=> 35X-135 = 32X-108
=> 35X-32X = -108+135
=> 3X = 27
=> X = 27/3
=> X = 9
Now,
If X = 9 then 8X = 8×9 = 72 years
The present age of A = 72 years
If X = 9 then 7X = 7×9 = 63 years
The present age of B = 63 years
72 > 63
A is the elder
Answer:-
The age of elder one (A) is 72 years
Check:-
A' s present age = 72 years
B' s present age = 63 years
Their ratio = 72:63
=> 72/63
=> (8×9)/(7×9)
=> 8/7
=> 8:7
27 years ago their ages
=> 72-27 = 45 years
and 63-27 = 36 years
The ratio of their ages = 45:36
=> 45/36
=> (5×9)/(4×9)
=> 5/4
=> 5:4
Verified the given relations in the given problem.
Used formulae:-
- a:b can be written as a/b