(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same - Maths - Comparing Quantities

Question

(x-2) men can do a piece of work in x days and (x+7) men can do 75%
of the same work in (x-10) days Then, in how many days (x+10) men
finish the work?

Atul Shaw · Accepted Answer

Dear student,(x-2) can do a piece of work in x days
(x+7) men can do 75% of same work in (x-10) days
Total work= Total men×Total timeTotal work= (x-2)x75% of total work = (x+7)(x-10)⇒75100× (x-2)x=(x+7)(x-10)⇒34× (x-2)x=(x+7)(x-10)⇒3(x2-2x)=4(x2-10x+7x-70)⇒3x2-6x=4x2-12x-280⇒x2-6x-280=0⇒x2-20x+14x-280=0⇒x(x-20)+14(x-20)=0⇒(x+14)(x-20)=0x=-14,20x can't be negative because the man can't be in negative in number
so, x=20Total work=(x-2)x=(20-2)20=360unitNow, total men=x+10=20+10=30Total time=36030=12daysRegards

(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10) days. Then, in how many days (x+10) men finish the work?