Question

The number of days required to build a bridge varies inversely with the number of workers. If 10 workers took 16 days to complete building the bridge, how many days will it take for 15 workers to build the same bridge?​

Answer 1

Answer:

11

Step-by-step explanation:

Let no. of days required to build bridge be x and no. of workers be y.

$x ∝ \frac{1}{y}$

Since, x & y are inversely proportional

$x_1y_1 = x_2y_2$

According to question,

$(16) \times (10) = x_2(15) \\ \\ x_2 = \frac{16 \times 10}{15} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = \frac{16 \times 2}{3}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = \frac{32}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = 10.66\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2≈ 11 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

We know that no. of days (x) can't be in the decimal form. So, approximately no. of days = 11 days.

∴ 11 days will be required for 15 workers to build same bridge.