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Time and Work — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsTime and Work1 Mark
MCQ
Tick the correct answer in the following: $A$ does $20\%$ less work than $B.$ If $A$ can finish a piece of work in $7\frac{1}{2}$ hours, then $B$ can finish it in:
  • A
    $5\ \text{hours}.$
  • B
    $5\frac{1}{2}\ \text{hours}.$
  • ✓
    $6\ \text{hours}.$
  • D
    $6\frac{1}{2}\ \text{hours}.$
✓

Answer

Correct option: C.
$6\ \text{hours}.$
$A's$ hour's work $=\frac{2}{15}$
$A$ and $B's$ ratio in work $=\frac{100-20}{100}:1$
$=\frac{80}{100}:1$
$=\frac{4}{5}:1$
Let ratio be, $\frac{4}{5} x$ and $x,$ then,
$\frac{4}{5}:1=\frac{2}{15}:\frac{1}{\text{x}}$
$1\times\frac{2}{15}=\frac{4}{5}\times\frac{1}{\text{x}}=\frac{2}{15}=\frac{4}{5\text{x}}$
$2\times5\text{x}=4\times15$
$\Rightarrow\text{x}=\frac{4\times15}{2\times5}=6$
$\therefore B$ can finish the work in $6$ hours.

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