Question 16: Profit/Loss Percentage Cost price of 80 notebooks is equal to the selling...

The question asks for the present age of the daughter based on a system of linear equations derived from the given age relationships. Solving the system yields the daughter's age as 23 years.

Step-by-step Derivation:
Step 1: Define variables. Let P = Pranathi's present age, S = Son's present age, D = Daughter's present age, and H = Husband's present age.
Step 2: Translate the statements into equations:
(i) Eight years ago, Pranathi's age was equal to the sum of the present ages of her son and daughter: P - 8 = S + D.
(ii) Five years hence, the ratio of daughter's age to son's age will be 7:6: (D + 5) / (S + 5) = 7 / 6.
(iii) Husband is 7 years older than Pranathi: H = P + 7.
(iv) Husband's present age is three times the son's present age: H = 3S.
Step 3: Substitute (iii) into (iv): P + 7 = 3S, which means P = 3S - 7.
Step 4: Substitute P = 3S - 7 into equation (i): (3S - 7) - 8 = S + D => 2S - 15 = D.
Step 5: Substitute D = 2S - 15 into equation (ii): (2S - 15 + 5) / (S + 5) = 7 / 6 => (2S - 10) / (S + 5) = 7 / 6.
Step 6: Solve for S: 6(2S - 10) = 7(S + 5) => 12S - 60 = 7S + 35 => 5S = 95 => S = 19.
Step 7: Find D using D = 2S - 15: D = 2(19) - 15 = 38 - 15 = 23.
Step 8: The present age of the daughter is 23 years.