Abha and Anuj working together completed a job in \(40\over9\) days. If Abha had worked twice as efficiently as she actually did and Anuj had worked \(1 \over 3\) of his actual efficiency, then the work would have been completed in \(60 \over 17\) days. Find the time Abha would take to complete the work alone

Given:

Abha and Anuj working together completed a job in\(40\over9\) days.

Formula Used:

Total units of work. = Total number of days × Total Efficiency

​​\(\frac{{M1.D1.T1.E1}}{{W1.C1}} = \;\frac{{M2.D2.T2.E2}}{{W2.C2}}\)

Where,

M is the number of working men

D is the total number of days

T is total hours of working days

E is the efficiency of working men

W is total work

C is the consumption of working men

Calculation:

According to the question,

In both cases, they have worked equal units of work, 

Using the formula,

⇒ (Abha + Anuj) × 40/9 = [(2 × Abha) + (1/3 × Anuj)] × 60/17

⇒ 34 Abha + 34 Anuj = 54 Abha + 9 Anuj

⇒ 25 Anuj = 20 Abha

⇒ 5 Anuj = 4 Abha

The ratio of efficiency, 

⇒ Abha = 5 units/day & Anuj = 4 units/day

Total units of work, 

Total units of work. = Total number of days × Total Efficiency

⇒ (5 + 4) × 40/9 = 40 units 

Total number of days = Total units of work/Efficiency

Total number of days required by Abha to complete the work,

⇒ 40/5 = 8 days

Total number of days required by Abha to complete the work is 8 days.