Question

In what time will Rs. 500 amount to Rs. 750 at 12% p.a. simple interest?

3 years 8 months
4 years
4 years 2 months
4 years 8 months

Answer 1

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Option C

In 4 years 2 months, Rs. 500 will amount to Rs. 750 at 12% p.a. simple interest.

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Given :-

• Principal (P) = Rs. 500
• Amount (A) = Rs. 750
• Rate % (R) = 12 % p.a.

To Find :-

• Time (T)

Solution :-

Interest = Amount - Principal

⇒ Rs. 750 - Rs. 250

⇒ Rs. 250

Interest = Rs. 250

Simple Interest = Principal × $\frac{Rate}{100}$ × Time

⇒ Rs. 250 = Rs. 500 × $\frac{12}{100}$ × Time

⇒ Rs. 250 = Rs. 60 × Time

⇒ Time = $(\frac{Rs.250}{Rs.60})years$

➠ Time = $4\frac{1}{6} years$

✧ $4\frac{1}{6} years$ = 4 years 2 months

✧ Time = 4 years 2 months

• Hence, In 4 years 2 months, Rs. 500 will amount to Rs. 750 at 12% p.a. simple interest.

Let's verify :-

Amount = (Principal × $\frac{Rate}{100}$ × Time) + Principal

↦ Rs. 750 = (Rs. 500 × $\frac{12}{100}$ × $4\frac{1}{6} \ years$) + Rs. 500

↦ Rs. 750 = (Rs. 60 × $\frac{25}{6} \ years$) + Rs. 500

↦ Rs. 750 = Rs. 250 + Rs. 500

↦ Rs. 750 = Rs. 750

➦ LHS = RHS

Hence, Verified ✔

Answer 2

Answer: The correct answer is option C, 4 years 2 months.

Step-by-step explanation:

To calculate the time taken for Rs. 500 to amount to Rs. 750 at 12% p.a. simple interest, we can use the formula:

Simple Interest = (Principal x Rate x Time) / 100

Where,

Principal = Rs. 500

Amount = Rs. 750

Rate = 12% p.a.

Substituting the values in the formula, we get:

Simple Interest = (500 x 12 x Time) / 100

Simple Interest = 60Time/100

Since the simple interest is the difference between the amount and principal, we can also write:

Simple Interest = Amount - Principal

60Time/100 = 750 - 500

60Time/100 = 250

Time = (250 x 100) / 60

Time = 416.67 months

Therefore, the time taken for Rs. 500 to amount to Rs. 750 at 12% p.a. simple interest is approximately 416.67 months. Converting this to years and months, we get:

416.67 months = 34 years and 8 months

However, since the question only asks for the time in years and months, we can round off the answer to the nearest month, which gives us:

4 years and 2 months

Therefore, the correct answer is option C, 4 years 2 months.

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