Raman is three times as efficient as Manan. Raman can complete a work in 60 days less than Manan. In how many days the work will be completed if both of them work together ?

Let the time taken by Raman in doing 1 work be x days. ∴ Time taken by Manan = 3x days According to the question, 3x – x = 60 $Rightarrow 2 x=60$ $Rightarrow x=frac{60}{2}=30$ days $herefore$ (Raman $+$ Manan)’s 1 day’s work $=frac{1}{30}+frac{1}{90}=frac{3+1}{90}=frac{4}{90}$ $herefore$ Required time $=frac{90}{4}=22.5$ days Alternative: $left(ecause ight.$ Efficiency $left.alpha=frac{1}{ ext { Time }} ight)$ 3 – 1 = 2 unit = 60 days 1 unit = 30 days 3 unit = 30 × 3 = 90 days

( $ecause$ Total work = Time $imes$ Efficiency)

$herefore$ Time taken by both to complete the work

$=frac{ ext { Total work }}{ ext { Efficiency of both }}$

$=frac{90}{3+1}=22.5$ days