If a person has some flowers and he put some of them in a temple and rest he doubles and put some in another temple and doubles the rest and put all of them in third temple if flowers in all the temples are equal then what is the number of flower the person was having in the starting
Answers
Answer:
27
Let's say the man threw x flowers into the lake. Then he has 3x flowers and puts y of them into the first temple, leaving him with 3x−y flowers.
He throws them in again, resulting in 9x−3y flowers, and puts y of them in the temple again, for 9x−4y flowers.
He throws them in a third time resulting in 27x−12y flowers, and puts y of them in the temple, for 27x−13y=0 flowers.
The smallest integer solution that will work here is
x=13, y=27, so the man had 13 flowers initially and put 27 flowers in each temple.
In general, this sort of problem is called an annuity problem, and has applications in finances when calculating amortization rates of mortgages (hence the term "annuity problem"). In the above example, an equivalent problem using loans would be that you have a debt of $13 with an annual interest rate of 200% that you want to pay off in 3 years, which requires a payment of $27 every year. To calculate the payments required, the following formula is used:
p=P(1+i)n1+(1+i)+(1+i)2+(1+i)3+…+(1+i)n−1=P(1+i)ni(1+i)n−1
where p is the periodic payment, P is the initial principal amount, n is the number of pay periods, and i is the interest rate per pay period. In the problem statement above, i=2 and n=3, so the ratio of flowers put into each temple to initial flowers is 27/13 (p=P(2+1)3(2)(2+1)3−1=54P26=2713P), which is consistent with what working it out manually gave us.
You'll notice with the above formula that any multiple of 13 flowers would work, if you put the same multiple of 27 flowers into each temple. If you allowed for fractional flowers, you could start with 1 flower and put 27/13 flowers into each temple and it would work out the same way.
Answer:
Don't worry The answer is 15