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Joint Entrance Examination
Mathematics
Quadratic Equations and Inequalities
Question 12
Question 12 of 157
Medium
MCQ
A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :
A
36 days
B
24 days
C
30 days
D
42 days
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Solutions · 1
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Official solution
=
x
=x
=
x
⇒
=
(
x
−
24
)
A
=
1
x
−
24
B
=
1
x
1
x
−
24
+
1
x
=
1
22.5
2
x
−
24
x
(
x
−
24
)
=
1
22.5
45
x
−
540
=
x
2
−
24
x
x
2
−
69
x
+
540
=
0
(
x
−
60
)
(
x
−
9
)
=
0
⇒
x
=
60
=
60
−
24
=
36
\begin{gathered} \Rightarrow =(x-24) \\ A=\frac{1}{x-24} \\ B=\frac{1}{x} \\ \frac{1}{x-24}+\frac{1}{x}=\frac{1}{22.5} \\ \frac{2x-24}{x(x-24)}=\frac{1}{22.5} \\ 45x-540={x}^{2}-24x \\ {x}^{2}-69x+540=0 \\ (x-60)(x-9)=0 \\ \Rightarrow x=60 \\ =60-24 \\ =36 \end{gathered}
⇒=
(
x
−
24
)
A
=
x
−
24
1
B
=
x
1
x
−
24
1
+
x
1
=
22.5
1
x
(
x
−
24
)
2
x
−
24
=
22.5
1
45
x
−
540
=
x
2
−
24
x
x
2
−
69
x
+
540
=
0
(
x
−
60
)
(
x
−
9
)
=
0
⇒
x
=
60
=
60
−
24
=
36
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