A student measured the length of a room and obtained the measurement of 3.99m. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room?
A
3.78m
B
3.80m
C
4.18m
D
4.20m
E
4.788m
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Let the actual length of the room = y m
\(\therefore \frac{y - 3.99}{y} \times 100 = 5%\)
\(100(y - 3.99) = 5y \implies 100y - 399 = 5y\)
\(100y - 5y = 399 \implies y = \frac{399}{95}\)
y = 4.2 m
Source: Myschool Past Questions Archive (Record #22099)