$12$ painters can paint a wall of $180 m$ long in $3$ days. How many painters are required to paint $200 m$ long wall in $5$ days?

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Solution

Here number of painters are in direct proportion to length the wall and inversely proportional to number of days.
No. of painter Length of wall (m) No. of days
$12$ $180$ $3$
$x$ $200$ $5$
$12 : x$ $180 : 200 = 9 : 10$ $3 : 5$
Number of painters $α$ length of the wall
$12 : x = 9 : 10$ ......... (1) and
Number of painters $α \frac{1}{n u m b e r o f d a y s}$
$12 : x =$ inverse ratio of $3 : 5$
$12 : x = 5 : 3$ ........(2)
from (1) and (2)
$12 : x =$ compound ratio of $9 : 10$ and $5 : 3$
$12 : x = (9 : 10) \times (5 : 3)$
$12 : x = 9 \times 5 : 10 \times 3$
$12 : x = 45 : 30 = 3 : 2$
$3 \times x = 12 \times 2$
$x = \frac{24}{3} = 8$
Number of painter required $= 8$

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