|
 EXAMPLES
IN QUANTITATIVE MATHEMATICS
Percentages
Definition : A percentage is a fraction with denominator always
100. So fraction and percentages are inter convertible. To convert
a fraction it is to be multiplied with 100.
To convert a percentage it is to be divided with 100.
Example 1: 1/2 = 1/2 x 100 = 50%.
Example 2: 3/4 = 3/4 x 100 = 75%.
Example 3: 50% = 50/100 = 1/2.
Example 4: 75% = 75/100 = 3/4.
Time & Work
In solving the problems in time and work we have to remember the
following facts.
- If a man can do a piece of work in 20 days, he will do 1/20th
of the work in 1 day and conversely, if a man can do 1/20th of
the work in 1 day, he will finish the work in 20 days.
- If the number of men engaged to do a piece of work be changed
in the ratio 6:5, then the time required for the work will be
changed in the ratio 5:6.
- If A does twice as good work as B, then A will take half of
the time that B takes to do a certain work.
| Exercise -1: |
A can do a piece of work in 6 days and B can
do it in 4 days. How long will they take if they both work
together. |
| Solution: |
A + B can do the work by = 1/6 + 1/4 = 10/24 = 5/12.
Therefore A & B can do all the work in 12/5 = 2 2/5 days. |
| Exercise -2: |
A & B together can do a piece of work in 4 days and A
alone can do it in 6 days. In how many days can B do it? |
| Solution: |
A + B can do 1/4 of the work in 1 day
A alone can do 1/6 of the work in a day
B alone can do in 1/4 - 1/6 =1/12 of the work in 1 day
B alone can do the whole work in 12 days. |
Profit and Loss
- Definition : Profit = Selling Price - Cost Price
[Selling price more than the cost price]
- Loss = Cost Price - Selling Price
[Cost Price is more than the selling price]
The profit or loss is generally calculated on the cost price
only.
- In the case of gain, Selling Price = Cost Price + Profit
- In the case of loss, Selling Price = Cost Price - Loss
- Selling Price = Cost Price x (100 + profit %) / 100 When
the profit % is given
- Selling Price = Cost Price x (100 - loss %) / 100 When
the loss % is given
- Cost Price = Selling Price x 100 / 100 + profit
- Cost Price = Selling Price x 100 / 100 - loss %
- Gain Percentage = Gain x 100 / Cost Price
- Loss Percentage = Loss x 100 / Cost Price
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