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Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes. Quantity 2: A sum of Rs. 725 is lent at the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest? Quantity 3: The difference between the compound interest and the simple interest on an amount of 15000 for 2 years is Rs. 96. What is the rate of interest per annum?

Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes. Quantity 2: A sum of Rs. 725 is lent at the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest? Quantity 3: The difference between the compound interest and the simple interest on an amount of 15000 for 2 years is Rs. 96. What is the rate of interest per annum? Correct Answer If Quantity 1 is maximum

Quantity 1:

Let the sum be Rs. 100. Then,

⇒ S.I. for first six months = = Rs. 5

⇒ S.I. for next six months = = Rs. 5.25

⇒ So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

⇒ Effective rate = (110.25 – 100) = 10.25%

Quantity 2:

let the original rate be r%

Then the new rate will be 2r%

⇒ (725 × r × 1)/100 + (362.50 × 2r × 1)/100 × 3 = 33.50

⇒ (2175 + 725) r = 33.50 × 100 × 3 = 10050

⇒ r = 10050/2900 = 3.46%

⇒ Original rate = 3.46%

Quantity 3:

Let the interest be r%

Difference between SI – CI

⇒ – = 96

⇒15000 × = 96

⇒ 15000 × = 96

⇒ r2 = 96 × 2/3 = 64

⇒ r = 8%

Comparing all three quantities

∴ Quantity 1 > Quantity 3 > Quantity 2

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An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes---