# A face mask has to be designed in the shape of a rectangle to cover the nose and mouth. But while material testing it was found that after every wash the material shrunk by 10% of its area. Find the amount of material used for the mask if it can only be used for 3 washes and at the end of the third washes it is 10 cm × 8 cm.(approx.)

1. 10 × 11

2. 5 × 22
3. 22 × 5
4. 11 × 10
5. None of the above

Option 4 : 11 × 10

## Detailed Solution

Given:

After every wash material shrunk by 10% its area

Maximum number of washes = 3

Dimensions after fourth wash = 10 cm × 8 cm

Calculation:

Let the length and breadth of the material initially be l and b respectively.

Then, initial area, A = l × b

After every wash reduction in area = 10% of area

After first wash, area remaining = (100 – 10)% of the area

⇒ Area after first wash = 90% of A

After second wash, area remaining = (100 – 10)% of area after first wash

⇒ Area after second wash = 90% of 90% of A

After third wash, are remaining = (100 – 10)% of area after second wash

⇒ Area after third wash = 90% of 90% of 90% of A

⇒ 90% of 90% of 90% of A = 10 × 8

⇒ 90/100 × 90/100 × 90/100 × A = 80

⇒ 9/10 × 9/10 × 9/10 × A = 80

⇒ A = (80 × 10 × 10 × 10)/(9 × 9 × 9)

⇒ A ≈ 110 cm2

Then, one of the possible values of length and breadth of the initial material to attain area A is 11 cm × 10 cm.

∴ The required possible dimensions of the initial mask will be 11 cm × 10 cm.
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