1. The price of petrol is increased by
25%. By what percent the consumption be reduced to make the expenditure remain
the same?
a.
25% b. 33.33% c. 20% d. None
2. If the length of a rectangle is
increased by 33.33%, by what percentage should the breadth be reduced to make
the area same?
a. 20% b. 33.33% c. 25% d. None
Have the below list::::::::::::::::
10% 0.1 1/10
12.5% 0.125 1/8
16.66% 0.1666 1/6
20% 0.2 1/5
25% 0.25 1/4
30% 0.3 3/10
33.33% 0.3333 1/3
40% 0.4 2/5
50% 0.5 1/2
60% 0.6 3/5
62.5% 0.625 5/8
66.66% 0.6666 2/3
70% 0.7 7/10
75% 0.75 3/4
80% 0.8 4/5
83.33% 0.8333 5/6
90% 0.9 9/10
100% 1.0 1
Short trick for above problems:
in first problem,he want to bring
back the original value,so need to decrease the value.
price increased,so became–25%
in the above list,see the next
decreased value from 25% IS 20% so yopur answer is 20%
in second problem
increased value——–33.33%
next decreased value–30%,SO ANSWER IS
30%
Percentage Change:
A change can be of two types – an
increase or a decrease.
When a value is changed from initial
value to a final value,
% change = (Difference between
initial and final value/initial value) X 100
Eg: If 20 changes to 40, what is the
% increase?
Soln: % increase = (40-20)/20 X 100 =
100%.
Note:
1. If a value is doubled the percentage increase is
100.
2. If a value is tripled, the percentage change is 200
and so on.
Percentage Difference:
%
Difference = (Difference between values/value compared with) X 100.
Eg:
By what percent is 40 more than 30?
Soln:
% difference = (40-30)/30 X 100 = 33.33%
(Here
40 is compared with 30. So 30 is taken as denominator)
Eg:
By what % is 60 more than 30?
Soln:
% difference = (60-30)/30 X 100 = 100%.
(Here
is 60 is compared with 30.)
Hint:
To calculate percentage difference the value that occurs after the word “than”
in the question can directly be used as the denominator in the formula.
So,
by now we came to know that if CP is increased and sold it would result in
profit and vice versa.
Also
whatever increase is applied to CP, that increase itself is the profit.
For
Rs. 10 profit, CP is to be increased by RS. 10 and the increased price becomes
SP.
For
10% profit, CP is to be increased by 10% and it is the SP.
(From
previous chapter we know that any value increased by 10% becomes 1.1 times.)
So, for 10% profit, CP increased by 10%
=> 1.1CP = SP.
·
SP
= 1.1CP => SP/CP = 1.1 => 10% profit
·
SP
= 1.07CP => SP/CP = 1.07 => 7% profit
·
SP
= 1.545CP => SP/CP = 1.545 => 54.5% profit and so on.
Similarly,
·
SP
= 0.9CP => SP/CP = 0.9 => 10% loss (Since 10% decrease)
·
SP
= 0.76CP => SP/CP = 0.76 => 24% loss and so on.
So, to
calculate profit % or loss %, it is enough for us to find the ratio of SP to
CP.
Note:
1.
If SP/CP > 1, it indicates profit.
2.
If SP/CP < 1, it indicates loss.
Multiple Profits or losses:
A
trader may sometimes have multiple profits or losses simultaneously. This is
equivalent to having multiple changes and so all individual changes are to be
multiplied to get the overall effect.
Relationship among CP, SP and MP:
A
trader adds his profit to the investment and sells it at that increased price.
Also
he allows a discount on Marked Price and sells at the discounted price.
So,
we can say that,
SP
= CP + Profit. (CP applied with profit is SP)
SP
= MP – Discount. (MP applied with discount is SP)
Q:
A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his
profit/loss %.
Soln:
1 kg weight for 800 gm => loss (decrease) => 800/1000 = 0.8
20%
increase in price => profit (increase) => 1.2
So,
net effect = (0.8) X (1.2) = 0.96 => 4% loss.
2. A milk vendor mixes water to milk such
that he gains 25%. Find the percentage of water in the mixture.
Soln:
To gain 25%, the volume has to be increased by 25%.
So,
for 1 lt of milk, 0.25 lt of water is added => total volume = 1.25 lt
%
of water = 0.25 / 1.25 X 100 = 20%.
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