Aman distributed 80% of his total money between Kavya and Aryan in the ratio 3 : 5. Kavya invested her share at 9% p.a. and Aryan at 6% p.a. simple interest for 6 years. If the difference in the interest earned by Aryan and Kavya is Rs. 2,592, then what is the total amount Aman had?
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Correct answer: A
Explanation
Given:
Aman divided 80% of his total amount.
Kavya : Aryan = 3 : 5
Kavya's interest = 9%
Aryan's interest = 6%
Time = 6 years
Difference in interest = 2592
By formula:
SI = (P × R × T) / 100
Let Aman's total amount = x
Amount divided = 0.8x
Kavya's share = (3/8) × 0.8x = 0.3x
Aryan's share = (5/8) × 0.8x = 0.5x
Kavya's interest = (0.3x × 9 × 6) / 100 = 0.162x
Aryan's interest = (0.5x × 6 × 6) / 100 = 0.18x
Difference = 0.18x − 0.162x = 0.018x
0.018x = 2592
x = 2592 / 0.018
x = 144000
Aman's total amount = ₹144000