A certain sum of money becomes three times of itself in 5
2
1
​
years at a certain rate of simple interest. How much time will it take to become six times of itself at the same rate?

Let the principal sum be P.
In the first case, the amount becomes 3P.

Simple Interest (SI
1
​
)=3P−P=2P
Time taken (T
1
​
) =5
2
1
​
years=
2
11
​
years

In the second case, the amount becomes 6P.

Simple Interest (SI
2
​
)=6P−P=5P
Let the time taken be T
2
​
.

Since the rate of interest is the same, the simple interest is directly proportional to time:

SI
2
​

SI
1
​

​
=
T
2
​

T
1
​

​

5P
2P
​
=
T
2
​

2
11
​

​

5
2
​
=
2×T
2
​

11
​

4×T
2
​
=55⟹T
2
​
=
4
55
​
years
Converting into years and months:

T
2
​
=13
4
3
​
years=13years+(
4
3
​
×12)months=13years and 9months