1. 

In how many years will a sum of money put at simple interest treble itself ?

I. The interest earned in 4 years is half the sum.

II. The rate of interest is 12%.

III. The sum doubles itself in 8 years at simple interest.
A. I and II only
B. II and III only
C. All I, II, and III
D. Any one of the three
E. Any two of the three

Answer: Option D

Explanation:

Let sum be ₹ X. Then,
S.I. = ₹ (3X - X) = ₹ 2X, T = ?

I gives : When T = 4, then S.I. = ₹ X/2.

 Rate = 100 x S.I. %
P x T

= (100 x X/2 x 1/X x 1/4)

= 12% p.a.

Now Sum = ₹ X, S.I. = ₹ 2X, R = 25% p.a., T = ?

Time = 100 x 2X x 2 years = 16 years.
X x 25

Thus, I only gives the answer.

II gives, R = 25% p.a.

Time = 100 x 2X x 2 years = 16 years.
X x 25

Thus, II only also gives the answer.

III gives, R = 5% p.a.

Time = 100 x 2X years = 40 years.
X x 5

Thus, III only also gives the answer.

Correct answer is (D)