Final Answer:
a) P's share is ₹36,000.
b) Q's share is ₹30,000.
Step-by-step explanation:
Let P's share be x rupees, then Q's share is 66,000 - x rupees. Using the compound interest formula, P's amount at 12 years would be x × (1 + 0.20)⁴ , and Q's amount at 12 years would be (66,000 - x) × (1 + 0.20)³ . Given that both amounts are equal at 12 years:
x × (1.20)⁴ = (66,000 - x) ×(1.20)³
Solving the equation:
x × 1.44 = 66,000 × 1.20 - x × 1.20
1.44x + 1.20x = 79,200
2.64x = 79,200
x = 79,200 / 2.64
x = 30,000
Therefore, P's share is ₹36,000 (₹66,000 - ₹30,000) and Q's share is ₹30,000.
At the rate of 20% per annum compound interest, P's share grows to ₹36,000 and Q's to ₹30,000 when they reach 12 years old. This calculation is derived by equating the compounded amounts of their respective shares at the age of 12 years. The equation is set up using the compound interest formula and the fact that they receive equal amounts at 12 years.
By solving the equation, the value of P's share is found to be ₹36,000, which is the difference between the total amount and Q's share. Consequently, Q's share is computed as ₹30,000, which completes the distribution of the ₹66,000 between P and Q, in accordance with the given conditions and compound interest calculations.