Question

3 year ago , the ratio between p:q is 9:5 , after 2 years p's age will be 17 year more than that of age of q after 5 year . What is q's present age

Answer 1

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28 years

step-by-step explanation:

let the present ages of p and q be a and b respectively.

then,

age of both 3 years ago is,

(a-3) and (b-3) years respectively.

now,

A.T.Q,

(a-3)/(b-3) = 9/5

=> 5(a-3) = 9(b-3)

=> 5a - 9b = -12

=> 9b - 5a = 12 ..........(i)

Now,

p's age after 2 yrs = (a+2) yrs.

and,

q's age after 5 yrs = (b+5) yrs

but,

A.T.Q

(a+2) = (b+5) +17

=> a + 2 = b + 22

=> a - b = 20

multiplying the equation with 5,

we get,

=> 5a - 5b = 100 ................(ii)

Now,

adding the eqn (i) and (ii),

we get,

9b - 5b = 100+12

=> 4b = 112

=> b = 112/4

=> b = 28

But b is q's present age

Hence,

q's present age is 28 years.

Answer 2

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⏬⏬Answer is here ⏬⏬

28 years

step-by-step explanation:

let the present ages of p and q be a and b respectively.

then,

age of both 3 years ago is,

(a-3) and (b-3) years respectively.

now,

A.T.Q,

(a-3)/(b-3) = 9/5

=> 5(a-3) = 9(b-3)

=> 5a - 9b = -12

=> 9b - 5a = 12 ..........(i)

Now,

p's age after 2 yrs = (a+2) yrs.

and,

q's age after 5 yrs = (b+5) yrs

but,

A.T.Q

(a+2) = (b+5) +17

=> a + 2 = b + 22

=> a - b = 20

multiplying the equation with 5,

we get,

=> 5a - 5b = 100 ................(ii)

Now,

adding the eqn (i) and (ii),

we get,

9b - 5b = 100+12

=> 4b = 112

=> b = 112/4

=> b = 28

But b is q's present age

Hence,

q's present age is 28 years.

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