Abha and Anuj working together completed a job in$\frac{40}{9}$ days. If Abha had worked twice as efficiently as she actually did and Anuj had worked $\frac{1}{3}$ of his actual efficiency, then the work would have been completed in$\frac{60}{17}$ days. Find the time Abha would take to complete the work alone.
Answer & explanation
Correct answer: option 2
Formula used:
⇒ \(\frac{M_1\;×\;D_1\;×\;H_1\;×\;E_1}{E_2\;×\;D_2\;×\;H_2\;×\;E_2}\) = \(\frac{W_1}{W_2}\)
where, M = no. of working men, D = no. of days W= Total work, E = Efficiency, H = Total hours of the work,
⇒ According to the question,
⇒ In both cases, they have worked equal units of work,
Using the formula,
⇒ (Abha + Anuj) x \(\frac{40}{9}\) = [(2 xAbha) + (\(\frac{1}{3}\) x Anju)] x \(\frac{60}{17}\)
⇒ 34 Abha + 34 Anuj = 54 Abha + 9 Anuj
⇒ 25 Anuj = 20 Abha
⇒ 5 Anuj = 4 Abha
The ration of efficiency,
⇒ Abha : Arun = 5 : 4,
⇒ (5 + 4) x \(\frac{40}{9}\) = 40 units.
⇒ Total no. of days required by Abha to complete the work = \(\frac{40}{5}\) = 8 days