Problem 1 :
The production of rice increased by 50% from 1995 to 1996.By what percentage should the production of rice be increased from 1996 to 1997, so that the production of rice in 1997 becomes six times that of 1995?
Solution :
Let the production of rice be 100 tons in 1995.
1995 ----> 100 tons
Because the production has been increased by 50% in 1996 from 1995, we have
1996 ----> 150 toms
Because the production in 1997 becomes six times that of 1995, we have
1997 ---> 600 tons
When we look in to the above calculations, it is very clear that the production of rice has been increased by 450 tons 1997 from 1996.
Percentage increase 1997 from 1996 is
= (450/150) ⋅ 100%
= 300%
Hence percentage of rice production increased from 1996 to 1997 is 300%.
Problem 2 :
15% of income of A is equal to 25% of income of B and 10% of income of B is equal to 30% of income of C. If income of C is $ 1600, find the total income of A, B and C.
Solution :
Let A,B and C be the incomes of A,B and C respectively.
From the given information, we have C = $1600.
10% of B = 30% of C
(10/100) ⋅ B = (30/100) ⋅ 1600
B = $4800
So, the income of B is $4800.
15% of A = 25% of B
(3/20) ⋅ A = (1/4) ⋅ 4800
A = (20/3) ⋅ (1/4) ⋅ 4800
A = $8000
So, the income of B is $8000.
A + B + C = 8000 + 4800 + 1600
A + B + C = 14400
Hence, the total income of A, B and C is $14400.
Problem 3 :
The length of a rectangle is increased by 50%. By what percent would the width have to be decreased to maintain the same area?
Solution :
Let the length and width of the rectangle be 100 cm each.
Area of the rectangle = l ⋅ W = 100 ⋅ 100 = 10000 cm^{2}.
Given : The length of the rectangle is increased by 50%.
Let the width of the rectangle be decreased by P% to maintain the same area.
After changes,
length = 150
width = (100 - P)% of 100 = 100 - P
Even after the above two changes, area will be same
150 ⋅ (100 - P) = 10000
15000 - 150P = 10000
150P = 5000
P = 33.33%
Hence, the width has to be decreased by 33.33% to maintain the same area.
Problem 4 :
The production of wheat was increased by 20% from the year 1994 to 1995. It was further increased by 25% from 1995 to 1996. Find the the percentage change in the production of wheat from 1994 to 1996.
Solution :
Let the production of rice be 100 tons in 1994.
1994 ----> 100 tons
Because the production has been increased by 20% in 1994 to 1995, we have
1995 ----> 120 toms
Because the production has been increased by 25% in 1996 from 1995, we have
1996 ----> (100 + 25)% of 120
1996 ----> 125% ⋅ 120
1996 ----> 1.25 ⋅ 120
1996 ----> 150 tons
When we look in to the above calculations, it is very clear that the production of rice has been increased by 50% in 1996 from 1994.
Problem 5 :
The price of a table is $ 400 more than that of a chair. If 4 tables and 6 chairs together cost $3600, by what percentage is the price of the chair less than that of the table?
Solution :
Let x be the price of a chair.
Then the price of a table = x + 400.
4 tables + 6 chairs = 3600
4(x + 400) + 6x = 3600
4x + 1600 + 6x = 3600
10x = 2000
x = 200
So, the price of a chair is $400 and the price of a table is $800.
Price of a chair is $400 less than that of the table.
Percentage change = (400/800) ⋅ 100% = 50%.
Hence, the price of a chair is 50% less than that of the table.
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