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 can (x + 10) men finish the work?
(a) 27 days
(b) 12 days
(c) 25 days
(d) 18 days

Answer 1

Option 'b' is correct.

Step-by-step explanation:

Since we have given that

(x-2) men can do piece of work in x days

(x+7) men can do 75% piece of work in (x-10) days.

According to question, it becomes,

$(x-2)\times x=(x+7)\times (x-10)\times \dfrac{100}{75}\\\\3(x^2-2x)=4(x^2-3x-70)\\\\3x^2-6x=4x^2-12x-280\\\\x^2-6x-280=0\\\\x=-14,20$

So, (x+10) men can finish in days is given by

$(20+10)\times ?=(20-2)\times 20\\\\30\times ?=18\times 20\\\\?=12\ days$

Hence, Option 'b' is correct.

Answer 2

Given:   (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.

To Find :  in how many days can (x+10) men finish the work?

A) 27 days B) 12 days C) 25 days D) 18 days

Solution:

(x-2) men can do a piece of work in x days

=> Work  = x(x - 2)  man days

=> Work = x² - 2x man days

(x+7) men can do 75% of the same work in (x-10)days.

=> (75/100)Work  = (x + 7)(x - 10)  man days

=> (3/4) Work = x² - 3x  -70  man days

=>  Work  = (4/3)x² - 3x  -70  man days

x² - 2x =  (4/3)x² - 3x  -70

=> 3x² - 6x = 4x² - 12x - 280

=> x² - 6x  - 280 = 0

=> x² - 20x + 14x - 280 = 0

=> (x - 20)(x + 14) = 0

=> x = 20 , x = - 14

Work = x² - 2x man days

= 20² - 2(20)

= 400 - 40

= 360  man day

(x+10) men = 20 + 10 = 30 Men

Number of Days = 360/30  = 12

(x+10) men finish the work  in 12 Days

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