If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by? Class 8

If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by? Class 8

Question 1.

If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by? Class 8

Solution:

Let length and breadth be x and y respectively.

So, area = xy.

Let decrease percentage in breadth of d.

So. new area = x × [latex]\frac{110}{100}[/latex] × y ×[latex]\frac{(100-d)}{100} [/latex]

Therefore, xy × [latex]\frac{110}{100}[/latex] × [latex]\frac{(100-d)}{100}[/latex] = xy

or 110 (100 - d) = 10000

or 11000 - 110d = 10000

or 110d = 11000 - 10000

or 110d = 1000

So, d = [latex]\frac{1000}{110}[/latex]

= [latex]\frac{100}{11}[/latex] = 9[latex]\frac{1}{111}[/latex]%

Question 2.

The percentage of ingredients in a 65 g chips packet is shown in the picture. Find out the weight each ingredient makes up in this packet. Class 8

Solution:

Weight of potato

= 70% of 65 g

= [latex]\frac{70}{100}[/latex] × 65 g = 45.5 g

Weight of vegetable oil

= 24% of 65 g

= [latex]\frac{24}{100}[/latex] × 65 g = 15.6 g

Weight of salt = 3% of 65 g

= [latex]\frac{3}{100}[/latex] × 65 g = 1.95 g.

Weight of spices = 3% of 65

= [latex]\frac{3}{100}[/latex] × 65 g = 1.95 g.