The value of a number triples on the second day, decreases by half from second to third day. It then increases by half of the increase from the first day to the second day on the fourth day. If this cycle repeats and the value of the number is 375 after 10 days, what was the initial value (on first day)?
a. 18
b. 24
c. 30
d. 36
Answers
Question: The value of a number triples on the second day, decreases by half from second to third day. It then increases by half of the increase from the first day to the second day on the fourth day. If this cycle repeats and the value of the number is 375 after 10 days, what was the initial value (on first day)?
Solution: Acc to the question,
Let the number be "x" on the first day.
i.e. 1st day = x.
acc to the condition, 2nd day = 3x.
again on 3rd day = 1.5x
It then increases by half of the increase from the first day to the second day on the fourth day. i.e. on 4th day = (0.5 * 2x) + 1.5x = 2.5x
After 4 days the number becomes 2.5 times the intial number.
Day1: x
Day2: 3x
Day3: 1.5x
Day4: 2.5x
Day5: 7.5x
Day6: 3.75x
Day7: 6.25x
Day8: 18.75x
Day9: 9.375x
Day10: 15.625x
Acc to the question, 15.625x = 375.
Therefore, x = 24 i.e. Option B [Ans]
Given:
Number 375.
Conditions:
- Number triples on the second day.
- Number decreases by half on the third day.
- Number increases by half of the increase from the first day to the second day on the fourth day
To find:
The value of 375 after 10 days.
Solution:
Consider x be the number on the first day,
Then according to the conditions,
x, 3x, 1.5x, 2.5x, .... 15.625x
The value of the number is 15.625 on the 10th day.
Hence, 15.625x = 375
x = 24.
The answer is (b) 24.