Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone
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Let Pintu take = x days
Nishu takes = (x - 6) days
In one day
Pintu does = 1/x
Nishu does = 1/(x - 6)
The two together do 1/x + 1(x - 6), and they take 4 days;
So
1/x + 1(x - 6) = 1/4
8x - 24 = x² - 6x
x² -14 + 24 = 0
x² - 2x - 12x + 24 = 0
x(x - 2) - 12(x - 2) = 0
(x - 12)(x - 2) = 0
Either
x - 12 = 0
x = 12
or
x - 2 = 0
x = 2
x can not be 2, so we take x = 12
Pintu alone takes = 12 days
Nishu alone takes = 12 - 6 = 6 days
Nishu takes = (x - 6) days
In one day
Pintu does = 1/x
Nishu does = 1/(x - 6)
The two together do 1/x + 1(x - 6), and they take 4 days;
So
1/x + 1(x - 6) = 1/4
8x - 24 = x² - 6x
x² -14 + 24 = 0
x² - 2x - 12x + 24 = 0
x(x - 2) - 12(x - 2) = 0
(x - 12)(x - 2) = 0
Either
x - 12 = 0
x = 12
or
x - 2 = 0
x = 2
x can not be 2, so we take x = 12
Pintu alone takes = 12 days
Nishu alone takes = 12 - 6 = 6 days
I did not understand which method you use we have to form quadratic equations
Did you see this quadratic equation x² -14 + 24 = 0?
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