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A sum of money doubles itself in 25 years. The number of years it would trebles itself is:
- a)50 years.
- b)37.5 years.
- c)75 years.
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A sum of money doubles itself in 25 years. The number of years it woul...
Solution:
Let the sum of money be x.
Given, x doubles itself in 25 years.
So, after 25 years the amount becomes 2x.
Let y be the number of years it would treble itself.
Then, after y years the amount becomes 3x.
Now we can form a proportion:
2x : x :: 3x : ? (as the money doubles and trebles itself)
2x/x = 3x/? (cross multiply)
2 = 3x/? (cancel x)
? = 3x/2 (solve for ?)
Therefore, the amount would treble itself in 3x/2 years.
Now, substituting the value of x from the given information,
we get ? = 3(2x)/2 = 3x.
So, the amount would treble itself in 3x years.
Given, x doubles itself in 25 years.
Hence, 2x = x(2^1) = x(2^25/25)
Therefore, x = 25(2x/2^25) = 25x/2^24
So, x = (2^24)x/25
Or, 2^24 = 25
Taking log on both sides, we get
24 log2 = log25
Or, log2 = log25/24
Now, substituting the value of x in 3x, we get
3x = 3(25x/2^24) = 75x/2^24
Or, 3x = (2^24)(75x/2^24)/25
Or, 3x = (2^24)x/2^23
Or, 2^23 = 3
Taking log on both sides, we get
23 log2 = log3
Hence, the number of years it would treble itself is 23*25/Log2 = 50 years.
Therefore, the correct option is A.
Let the sum of money be x.
Given, x doubles itself in 25 years.
So, after 25 years the amount becomes 2x.
Let y be the number of years it would treble itself.
Then, after y years the amount becomes 3x.
Now we can form a proportion:
2x : x :: 3x : ? (as the money doubles and trebles itself)
2x/x = 3x/? (cross multiply)
2 = 3x/? (cancel x)
? = 3x/2 (solve for ?)
Therefore, the amount would treble itself in 3x/2 years.
Now, substituting the value of x from the given information,
we get ? = 3(2x)/2 = 3x.
So, the amount would treble itself in 3x years.
Given, x doubles itself in 25 years.
Hence, 2x = x(2^1) = x(2^25/25)
Therefore, x = 25(2x/2^25) = 25x/2^24
So, x = (2^24)x/25
Or, 2^24 = 25
Taking log on both sides, we get
24 log2 = log25
Or, log2 = log25/24
Now, substituting the value of x in 3x, we get
3x = 3(25x/2^24) = 75x/2^24
Or, 3x = (2^24)(75x/2^24)/25
Or, 3x = (2^24)x/2^23
Or, 2^23 = 3
Taking log on both sides, we get
23 log2 = log3
Hence, the number of years it would treble itself is 23*25/Log2 = 50 years.
Therefore, the correct option is A.
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Community Answer
A sum of money doubles itself in 25 years. The number of years it woul...
Assum that the sum is 100 i.e,after 25 years it will be 300
then the interest amount (S.I.) is 200
P=100,
ROI=100/25=4%,
T=?
S.I.= P*R(%)*T
200/(100*4%) = T
T=50 years
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