1.

1). 252). 243). 164). 19

Answer»

Let, T worked for ‘y’ DAYS.

⇒ R worked for (y - 8) days and S worked for (y - 12) days.

R completes the work in 36 days.

⇒ R’s 1 day’s work = 1/36

⇒ R’s (y - 8) day’s work = (y - 8)/36

S completes the work in 54 days.

⇒ S’s 1 day’s work = 1/54

⇒ S’s (y - 12) day’s work = (y - 12)/54

T can complete the work in 72 days.

⇒ T’s 1 day’s work = 1/72

⇒ T’s y day’s work = y/72

According to the QUESTION,

⇒ $(\FRAC{{y - 8}}{{36}} + \frac{{y - 12}}{{54}} + \frac{y}{{72}} = 1 \Rightarrow \frac{{6\left( {y - 8} \right) + 4\left( {y - 12} \right) + 3y}}{{216}} = 1)$

⇒ 13y - 96 = 216

⇒ 13y = 312

⇒ y = 24 days

∴ The number of days for which T worked = 24 days



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