Let’s
continue with this chapter............
Concept 4th :- (Questions
Based on Population)
Q15. If the annual increase in the
population of a town is 4% and present population is 15,625. What will be the population
after 3 years?
Sol.
Given the population of the town = 15,625
The annual
increase in the population of the town = 4%
Population
of the town after 1st year = (15,625) × {(100 + 4)/100}.
the
population of the town after 2nd year = (15,625) × (104/100) × {(100
+ 4)/100}.
the
population of the town after 3rd year = (15,625) × (104/100) ×
(104/100) × {(100 + 4)/100}.
Therefore,
: - (15,625) × (104/100) × (104/100) × (104/100)
On
simplifying we get:- Required population after 3 years = 26 × 26 × 26 = 17576.
Hence the Required population after
3 years = 26 × 26 × 26 = 17576.
Concept 5th :-
(Questions Based on Percentage increases and decreases.)
Note :- If
there is % increases or % decreases in any commodity/ price/ salary/ length etc
is given then the net resultant is obtained with the help of given equation:-
Net Resultant = ±(% increase or
decreases) ± (% increase or decreases) ± (Product of first two quantities with
their sign/100)
Where Sign
(+) is used for numeric quantities representing increase / hike / profit
While Sign
(-) is used for numeric quantities representing decrease / reduction / loss/ discount etc.
Example If the value of any item is increased
by x% and then after reduced by y% then the net resultant of that item is
calculated as:-
(+x) + (-y) + [{(+x) . (- y)}/100]
+x – y – (xy/100)
This trick
must be understood as it is a very important trick which very useful in various
chapters like profit loss, discount, Area etc including this chapter but always remember that this trick method
is used in the questions where only % values of increase and decrease are given and the net resultant is also
enquired in percentage only.
Q16. If the price of a commodity be
increased by 20%. By how much percentage must a man reduce his consumption so
that not to exceed his expenditure?
Note:- In such type of questions you
should analyse the question very carefully and implement the above trick
assuming net resultant zero (0) as it is given in the question that expenditure
should not increase.
Sol. Analyse the given data :-
Price increased by 20% means (+) sign will be
used with this data
Let a man
should reduce his consumption by x% means (-) sign must be used with it.
Net
resultant = 0 (zero)
Now as per
trick we will arrange the wanted equation for further calculation:-
(+20) +
(-x) + [{(+20) . (-x)}/100] = 0
+20 – x –
(20x/100) = 0
20 – x –
(x/5) = 0.
20 – (6x/5)
= 0
6x/5 = 20
x = 100/6 =
50/3 = 16whole(2/3).
Hence the man must reduce his
consumption by (50/3)% or [16whole(2/3)]%.
Q17. The price of sugar falls down by
10%. By how much a man should increase his consumption so as not to decrease
his expenditure.
Note:- In such type of questions you
should analyse the question very carefully and implement the above trick
assuming net resultant zero (0) as it is given in the question that expenditure
should not increase.
Sol. Analyse the given data :-
Price falls down means decreases by 10% means
(-) sign will be used with this data
Let a man
should increase his consumption by x% means (+) sign must be used with it.
Net
resultant = 0 (zero)
Now as per
trick we will arrange the wanted equation for further calculation:-
(-10) + (+x)
+ [{(-10) . (+x)}/100] = 0
-10 + x – (10x/100)
= 0
x – (x/10)
= 10.
9x/10 = 10
x = 100/9 = 11whole(1/9).
Hence the man must increase his
consumption by (100/9)% or [11whole(1/9)]%.
(Note you may say that this is so long but
dear this is the only way to explain the whole concept of the question to you
now its upto you that how fast and short handedly you can solve these type of
questions)
Hope you have enjoyed the base concept of this chapter till
now. More Conceptual enjoyment will be continued for you soon, just keep
visiting this blog regularly and writing me your related queries through
comment or forum.
More types
of questions will be followed soon on this blog........................
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