Math, asked by zeenathkhatoon26, 1 month ago

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

Answered by mandanageswararao9
2

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 .

Answered by tennetiraj86
7

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

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