Ex. A can do a piece of work in 10
days. B is 50 % more efficient than A. Find the number of days it takes B
to do the same piece of work ?
Solution : A : B
Efficency 100 : 150
Days 150 : 100
or 3 : 2
So the number of days taken by B to complete the work = ( 2 / 3 )* 10 = 6(2/3) days
Ex. Rs 450 is divided among 4 men , 5
women , and 6 boys such that the share of a man , a woman and a boy
may be in the ratio of 9 : 8 :4 . What is the share of a woman ?
Solution : The ratio of shares of group of men, women and boys =
9 * 8 : 8 * 5 : 4 * 6 = 36 : 40 : 24
Share of five woman will be ( 40 / 100 ) * 450 = Rs 180
So, share of a woman = 180 / 5 = Rs 36
Proportion :- If the two ratios are equal , the equality of a ratio are called proportion. Ex. 2 / 3 , 4 / 6
This proportion may be written as 2 : 3 :: 4 : 6
In this 2 and 6 are termed as extremes and the second and third terms are called means.
Rule : If the two ratios are in proportion then the product of extremes is equal to the product of means
Ex. 2 / 3 and 4 / 6
2 : 3 = 4 : 6 => 2 * 6 = 3 * 4
Rule: For continued proportion of three quantities a, b, c ratio of a : b = b : c
Ex. Find the mean proportional between 4 and 64
Soluion : 4 : x :: x : 64
So x = (4 * 64 )^ 1/2 = 16
Inverse Proportion :In this proportion if one of the term is increased corresponding term decreased. For better understanding see the example
Ex. If 15 men can reap a field in 28 days, in how many days will 10 men reap ?
Solution: Here if number of days decreased number of men will increased. So this is the example of inverse proportion.
1 / 15 : 1 / 10 :: 28 : The required number of days
10 : 15 :: 28 : The required number of days
In this case the required value = Multiplication of means / 1 st term , Place the required value at 4th place
Required Value = ( 15 * 28 ) / 10 = 42
Ex. A fort has food for 160 people
for 50 days. After 10 days, 20 people left the fort. How long the food
last at the same rate for the remaining people ?
Solution: This is also an example of inverse proportion, The remaining food will ast for 50 - 10 = 40 days
1/ 160 : 1/140 :: 40 : The required number of days
140 : 160 :: 40 : The required number of days
The required number of days =Multiplication of means / 1 st term = ( 160 * 40) / 140 = 45 days |
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