Question

A takes 10 days less than the time taken by B to finish
a piece of work. If booth A and B together can finish the
Work in 12 days, find the time taken
by
B to finish the
work
​

Answer 1

10 days time taken by the Booth B

Answer 2

Solution :

Let B take time on a piece of work be r day

A take time on a piece of work be (r - 10) day

⇒ B work done in one day = 1/r

⇒ A work done in one day = 1/r-10

$\underline{\boldsymbol{According\:to\:the\:question\::}}}$

If both A & B together finish the work in 12 day's, so for one day;

⇒ A + B = 1/12

$\longrightarrow\tt{\dfrac{1}{r-10} +\dfrac{1}{r} =\dfrac{1}{12} }\\\\\\\longrightarrow\tt{\dfrac{r+r-10}{r(r-10)} =\dfrac{1}{12} }\\\\\\\longrightarrow\tt{\dfrac{2r-10}{r^{2}-10r} =\dfrac{1}{12} }\\\\\\\longrightarrow\tt{12(2r-10)=1(r^{2}-10r)}\\\\\longrightarrow\tt{24r-120=r^{2}-10r}\\\\\longrightarrow\tt{r^{2}-10r-24r+120=0}\\\\\longrightarrow\tt{r^{2}-34r+120=0}$

$\underline{\boldsymbol{Using\:by\:quadratic\:formula\::}}}$

As we know that given quadratic polynomial compared with ax² + bx + c;

• a = 1
• b = -34
• c = 120

Now;

$\longrightarrow\bf{x=\dfrac{-b\pm\sqrt{b^{2}-4ac} }{2a} }\\\\\\\longrightarrow\tt{x=\dfrac{-(-34)\pm\sqrt {(-34)^{2}-4\times 1\times 120} }{2\times 1} }\\\\\\\longrightarrow\tt{x=\dfrac{34\pm\sqrt{1156-480} }{2} }\\\\\\\longrightarrow\tt{x=\dfrac{34\pm\sqrt{676} }{2} }\\\\\\\longrightarrow\tt{x=\dfrac{34\pm 26}{2} }\\\\\\\longrightarrow\tt{x=\dfrac{34+26}{2} \:\:\:Or\:\:\:x=\dfrac{34-26}{2}} \\\\\\\longrightarrow\tt{x=\cancel{\dfrac{60}{2}} \:\:Or\:\:x=\cancel{\dfrac{8}{2} }}$

$\longrightarrow\bf{x=30\:\:\:Or\:\:\:x=4}$

∴ x = 4 when we put the place of A value come's negative so it's not acceptable .

Thus;

Time taken by B to finish the worked = 30 day's .