Question

Arun makes a popular brand of ice-cream in a rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. to cut costs, the company had decided to reduce the volume of the bar by 19%. the thickness will remain the same, but the length and width will be decreased by the same percentage. the new width will be

Answer 1

new width will be 5 cm long and 3 cm wide

Answer 2

Answer:

The new width is $5-10 \times\frac{5}{100}=\frac{9}{2} =4.5 cm$

Step-by-step explanation:

Given that Arun makes a popular brand of ice-cream in a rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick.

Volume = $Length\times width\times height$

             = $6\times 5\times 2=60cm^{3}$

Now, to cut cost the company had decided to reduce the volume of the bar by 19%. Therefore, the new volume can be calculated as

New volume= $60-19% of 60=60-\frac{19}{100} \times 60=48.6 cm^{3}$

We have to find out the new width. To get new volume given the thickness will remain the same, but the length and width will be decreased by the same percentage.

⇒ Length = 6 - x% of 6

Breadth = 5 - x% of 5

Thickness = 2 cm

Hence, New Volume = ( 6 - x% of 6)( 5 - x% of 5)(2)

                     $48.6=(6-\frac{x}{100} \times 6)(5-\frac{x}{100} \times 5)2$

                   ⇒  $6(100-x)5(100-x)\times 2=486000$

                   ⇒  $(100-x)^{2}=8100$

                   ⇒ $x^{2} -200x+1900=0$

                   ⇒ $x=\frac{200\pm\sqrt200^{2}-4(1900) }{2}$

                   ⇒ x=10 is the possible solution

Hence, the new width is $5-10 \times\frac{5}{100}=\frac{9}{2} =4.5 cm$