Question

2

1. How long will it be (hours) until a silo filled with 50 tons of grain is half empty if the silo is emptying at the rate of 4% per hour?

Answer 1

Given,

The rate at which silo is emptying is 4% per hour.

The total amount of grains in the silo = 50 ton

Now,

we have to find the time taken for 50-ton silos to reduce to 25 ton

In one hour

the amount of ton reduce = 50 - 50*0.04

= 50*0.96 = 48

After the second hour

the amount of ton reduce = 48 - 48*0.04 = (50-50*0.04) - (50-50*0.04) *0.04 = (50*0.96)*0.96

If we look at the pattern it is forming a geometric progression as follows

50 *0.96*0.96*0.96.....nth term = 25

where n is the number of the hour at which the silo will reduce to 25

Therefore,

50 * 0.96^n = 25

0.96^n = 0.5

n log 0.96 = log 0.5

we need to have values of log 0.96 and 0.5 to find n

n * -0.01772 = -0.30102

n = 0.30102/ 0.01772 = 16.98 = 17 hours

We can also solve it using excel by goal seek formula