Find the Present Age of the Elder One
Sum of the ages of A and B is 7 times the difference in their ages, after 5 years the sum of the ages is 9 times the difference of their ages. The present age of the elder one is?
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As per 1st condition: A + B = 7 (A - B) -------------- (i)
As per 2nd condition,: A + 5 + b + 5 = 9 {(A + 5) - (B + 5)}
or A + B + 10 = = 9 (A - B)
or (A - B) = ( A + B + 10)/9 ------------------------------ ( ii)
Substituting the value we got in (ii) into (i), we get
A + B = 7{( A + B + 10)/9)
Simplifying this gives us A + B = 35 ------------------ (iii)
Putting (iii) in (i), we get 35 = 7(A - B)
From here we get A - B = 5 ------------------ (iv)
Adding (iii) and (iv), we get (A + B) + (A - B) = 35 + 5
Simplifying this gives us 2A = 40 and hence A = 20
Therefore, the present age of the older person is 20 years.
As per 2nd condition,: A + 5 + b + 5 = 9 {(A + 5) - (B + 5)}
or A + B + 10 = = 9 (A - B)
or (A - B) = ( A + B + 10)/9 ------------------------------ ( ii)
Substituting the value we got in (ii) into (i), we get
A + B = 7{( A + B + 10)/9)
Simplifying this gives us A + B = 35 ------------------ (iii)
Putting (iii) in (i), we get 35 = 7(A - B)
From here we get A - B = 5 ------------------ (iv)
Adding (iii) and (iv), we get (A + B) + (A - B) = 35 + 5
Simplifying this gives us 2A = 40 and hence A = 20
Therefore, the present age of the older person is 20 years.
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