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Algebra — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSAlgebra5 Marks
Question
Pari needs 4 hours to complete the work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?
✓

Answer

Pari: time required to complete the work $=4$ hrs.
$\therefore \ln 1$ hr. she will complete $=\frac{1}{4}$ of the work.
$
=\frac{1}{4} W
$

Yuvan: Time required to complete the work $=6$ hrs.
$\therefore$ In 1 hr. he will complete the $=\frac{1}{6}$ of the work
$
=\frac{1}{6} w
$

Working together, in $1 hr$. they will complete $\frac{ w }{4}+\frac{ w }{6}$ of the work.
$
\begin{aligned}
& =\frac{6 w+4 w}{24} \\
& =\frac{5}{12} w
\end{aligned}
$
$\therefore$ To complete the total work time taken
$
=\frac{ W }{\frac{5}{12} W }
$
$\begin{aligned} & =\frac{12}{5} \\ & =2.4 \text { hrs. ... }[\because(4) \text { hrs }=4 \times 60=24 min ] \\ & =2 \text { hrs } 24 \text { minutes. }\end{aligned}$

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