Lesson Business-related entertainment problem on percentage

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Business-related entertainment problem on percentage

Problem 1

A man borrowed from a bank under a promissory note that he signed in the amount of $25,000
for a period of one year. He received only the amount of $21,915 after the bank collected
the advance interest and additional amount of $85 for notarial and inspection fees.
What was the rate of interest that the bank collected in advance?

Solution

It is VERY simple problem, as you will see after reading my solution.

The amount of $25000 - $21915 = $3085 is the sum of the interest and  "the notarial and inspection fees".


THEREFORE, the interest after one year is  $3085 - $85 = $3000.


Now the rate of interest is   =  =  = 0.12 = 12%.


ANSWER.  The rate of interest is  0.12,  or  12%.

Solved.

Do you agree now that it is a simple problem ?

It is really simple, but a mental effort is needed to get an idea how to solve it.

Therefore, it can be considered as an entertainment problem.

Problem 2

Grace sells two sets of commemorative coins for $750 each. She gains 25% on one and lose 25% on the other.
Find the overall profit or loss percent.

Solution

Consider first coin.

Grace sells it for $750 and gains 25%.                                                           (1)


Let X be the price she BOUGHT  this coin some time ago.


Then the statement (1) means that she sold for the greater price, and

    750 - X = 0.25*X,   or  750 = 0.25*X + X = 1.25X;  hence  X =  = 600.


Thus Grace bought this coin for $600 and sold for $750, making profit of  $750 - $600 = $150.    (2)

Next consider second coin.

Grace sells it for $750 and lose 25%.                                                            (3)


Let Y be the price she BOUGHT  this coin some time ago.


Then the statement (1) means that she sold for the lesser price, and

    Y - 750 = 0.25*Y,   or  750 = Y - 0.25*Y = 0.75*Y;  hence  Y =  = 1000.


Thus Grace bought this coin for $1000 and sold for $750, losing $1000 - $750 = $250.             (4)



Hence, from (2) and (4), she gained $150 with first coin and lose $250 with second coin.


Overall, she lose  $250 - $150 = $100.


To find overall loss percent, we should relate these $100 to the sum  X + Y = $600 + $1000 = $1600.


Thus overall lose percent is   =  = 6.25%.     ANSWER

My other lessons on percentage problems in this site are
    - Percentage problems
    - Percentage word problems (Type 1 problems, Finding the Part)
    - Percentage word problems (Type 2 problems, Finding the Rate)
    - Percentage word problems (Type 3 problems, Finding the Base)
    - Simple percentage problems
    - More complicated percentage problems
    - Advanced problems on percentage
    - Percentage problems on chains of discounts
    - Problems on percentage that lead to unexpected results
    - Simple interest percentage problems
    - Compound interest percentage problems
    - Buying price, selling price and profit percentage problems
    - OVERVIEW of lessons on percentage problems

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