An icecream company makes a popular brand of icecream in a rectangular

1.	An icecream company makes a popular brand of icecream in a rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut costs, the company has decided to reduce the volume of the box by 20%. The thickness will remain the same, but the length and width will be decreased by the same percentage amount. Which condition given below will the new length l satisfy ? (a) 5.5 < l < 6 (b) 5 < l < 5.5 (c) 4.5 < l < 5 (d) 4 < l < 4.5
Answer» (b) 5 < l < 5.5. Original volume = (6 × 5 × 2) cm³ = 60 cm³ New volume = (60 – 20% of 60) cm³ = 48 cm³ Since the thickness remains the same, h = 2 cm ⇒ l × b × 2 = 48 ⇒ l × b = 24 New length = (6 – 10% of 6) cm = 5.4 cm New breadth = (5 – 10% of 5) cm = 4.5 cm Here l × b = 5.4 × 4.5 = 24.3 cm² ∴ l should clearly lie between 5 and 5.5, i.e., 5 < l < 5.5.

An icecream company makes a popular brand of icecream in a rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut costs, the company has decided to reduce the volume of the box by 20%. The thickness will remain the same, but the length and width will be decreased by the same percentage amount. Which condition given below will the new length l satisfy ? (a) 5.5 < l < 6 (b) 5 < l < 5.5 (c) 4.5 < l < 5 (d) 4 < l < 4.5

Answer»

(b) 5 < l < 5.5.

Original volume = (6 × 5 × 2) cm³ = 60 cm³

New volume = (60 – 20% of 60) cm³ = 48 cm³

Since the thickness remains the same, h = 2 cm

⇒ l × b × 2 = 48 ⇒ l × b = 24

New length = (6 – 10% of 6) cm = 5.4 cm

New breadth = (5 – 10% of 5) cm = 4.5 cm

Here l × b = 5.4 × 4.5 = 24.3 cm²

∴ l should clearly lie between 5 and 5.5, i.e., 5 < l < 5.5.