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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity I: The difference between the simple interest when the sum of Rs. 6000 is invested at the rate of interest of 15% for different M years and N years respectively is Rs. 2700. When the same sum is invested for N years at the rate of interest 30% on compound interest then compound interest is Rs. 4140. Find the value of M. Quantity II: When a number is divided by 11, the remainder is 5 and the same number is divisible by 14 then a reminder is 0. The difference between the quotients in both cases is 7. What should be remainder when twice the number is divisible by 10?

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity I: The difference between the simple interest when the sum of Rs. 6000 is invested at the rate of interest of 15% for different M years and N years respectively is Rs. 2700. When the same sum is invested for N years at the rate of interest 30% on compound interest then compound interest is Rs. 4140. Find the value of M. Quantity II: When a number is divided by 11, the remainder is 5 and the same number is divisible by 14 then a reminder is 0. The difference between the quotients in both cases is 7. What should be remainder when twice the number is divisible by 10? Correct Answer <span lang="EN-US" style=" line-height: 107%; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Quantity I &lt; Quantity II</span>

Quantity I:

Let P = principal, R = rate of interest and N = time period

Simple Interest = PNR/100

Compound interest = P(1 + R/100)n – P

⇒ 6000 × 15 × M/100 – 6000 × 15 × N/100 = 2700

⇒ 9M – 9N = 27

⇒ M – N = 3

⇒ 4140 = 6000(1 + 30/100)N – 6000

⇒ 1.69 = 1.3N

⇒ N = 2 years

⇒ M = 3 + 2 = 5 years

Quantity II:

Let number be N.

N = quotient A × 11 + 5

N = quotient B × 14 + 0

⇒ Quotient B × 14 = quotient A × 11 + 5

⇒ Quotient A – quotient B = 7

⇒ (quotient A – 7) × 14 = quotient A × 11 + 5

⇒ quotient A × 14 - 98 = quotient A × 11 + 5

⇒ Quotient A = 103/3

⇒ Quotient B = 124/3

⇒ N = 124/3 × 11 + 5 = 1379/3

⇒ 2N = 2 × 1379/3 = 2758/3

Remainder is 14 when 2758/3 are divided by 10.

So, we can observe Quantity I < Quantity II.

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