A work is assigned to total of 150 workers for a fixed days. 8 more da

1.	A work is assigned to total of 150 workers for a fixed days. 8 more days are required tocomplete that work if four workers are fail to work day by day constantly from the startingday, then after how many days the work finishes?OR
Answer» Let, 150 men would have completed the work in 'n' days working all days. Now no. of men & no. of days are inversely proportional. So, we get, 150n = constant ----------->(1) But, from 2nd day, 4 men left and so on and it took 8 days more than the normal to finish the work, ie, (n + 8) days. Consequently, 150 + 146 + 142 +.......to (n+8) terms = constant Left hand side is an A.P, with 1st term =150, common difference = -4 So, using formula, (n+8)1/2[2*150+(n+8-1)(-4)]= constant ------->(2) From equations, (n+8)[300+(n+7)(-4)]=300n Solving the quadratic equation, we get, n = 17, or -32(neglected) Hence, work is completed in, n+8 = 17 + 8 = 25 days

A work is assigned to total of 150 workers for a fixed days. 8 more days are required tocomplete that work if four workers are fail to work day by day constantly from the startingday, then after how many days the work finishes?OR

Answer»

Let, 150 men would have completed the work in 'n' days working all days.

Now no. of men & no. of days are inversely proportional. So, we get,

150n = constant ----------->(1)

But, from 2nd day, 4 men left and so on and it took 8 days more than the normal to finish the work, ie, (n + 8) days. Consequently,

150 + 146 + 142 +.......to (n+8) terms = constant

Left hand side is an A.P, with 1st term =150, common difference = -4

So, using formula,

(n+8)*1/2*[2*150+(n+8-1)(-4)]= constant ------->(2)

From equations,

(n+8)[300+(n+7)(-4)]=300n

Solving the quadratic equation, we get,

n = 17, or -32(neglected)

Hence, work is completed in,

n+8

= 17 + 8

= 25 days