Question

Henry had to paint some cartons. On the first day, the number of cartons he painted was 40% of the number of cartons that he had not painted. One week later, he painted another 100 cartons. As a result, the total number of painted cartons became 28 more than 1/2 of the total number of cartons. How many more cartons were unpainted than painted on the first day?

Answer 1

Let no. of Carton painted on first day = x.
no. of unpainted carton on first day = y
x = 40% of 8y = 40/100 * y = 0.4y
x = 0.4y — (1)
One week later, painted cartons = 100.
=> x + 100 = 28 + 1/2 (x + y) — (2)
Sub (1) in (2)
0.4y + 100 = 28 + 1/2 (y + 0.4y)
0.4y = 28 - 100 + 0.5y + 0.2y
(0.4 - 0.5 - 0.2)y = -72
-0.3y = -72 => y = 72/0.3
y = 240
x = 0.4 * 240 = 96
No. of painting cartons (1st day) = 96
No. of unpainted cartons = 240
Difference = 240 - 96 = 144
Answer = 144