Directions: Given below are two quantities. Based on the given information, you have to determine the relation between the two quantities. Quantity A: A man purchased a mobile valued Rs. 26040 from a dealer and promises to pay the amount in 3 equal installments at the rate of 12.5% per annum compou
Directions: Given below are two quantities. Based on the given information, you have to determine the relation between the two quantities.
Quantity A: A man purchased a mobile valued Rs. 26040 from a dealer and promises to pay the amount in 3 equal installments at the rate of 12.5% per annum compounded annually. Find the value of each installment.
Quantity B: A man borrowed a sum of Rs. 25000 from bank at 10% interest per annum. He pays back Rs. 10000 at the end of each year. Calculate how much amount he will have to pay at the end of 3rd year to clear his dues?1). Quantity A > Quantity B
2). Quantity A < Quantity B
3). Quantity A ≥ Quantity B
4). Quantity A ≤ Quantity B
1 answers
Quantity A:
Price of mobile = Rs. 26040 and rate of interest = 12.5% = 1/8
Let the amount of each installment is Rs. x and principals for three years are P1, P2 and P3.
First year:
x = P1 (1 + 1/8)
⇒ P1 = 8x/9
Second year:
x = P2 (1 + 1/8)2
⇒ P2 = 64x/81
Third year:
x = P3 (1 + 1/8)3
⇒ P3 = 512x/729
Sum of principle for 3 years = 26040.
∴ 8x/9 + 64x/81 + 512x/729 = 26040
⇒ 1736x/729 = 26040
⇒ x = 15 × 729
⇒ x = Rs. 10935
∴ Amount of each installment = Rs. 10935
Quantity B:
Man borrowed a sum of Rs. 25000 from bank at 10% interest per annum.
∴ Amount after 1 year = 25000 × 1.1 = Rs. 27500
Since he pays Rs. 10000 at the end of each year.
∴ Principal for second year = 27500 – 10000 = Rs. 17500
∴ Amount after 2 year = 17500 × 1.1 = Rs. 19250
Principal for third year = 19250 – 10000 = Rs. 9250
∴ Amount after 3 year = 9250 × 1.1 = Rs. 10175
∴ He will have to pay Rs. 10175 at the end of 3rd year to clear his dues.
∴ Quantity A > Quantity B