Given:
Hemant can complete the work in 7 days.
Irfan can complete the work in 19 days.
Hemant and Irfan worked together for 4 days.
Formula Used:
Work done by a person in 1 day = 1 / Total days to complete work.
Work done together in 1 day = Work done by Hemant in 1 day + Work done by Irfan in 1 day.
Work remaining = Total work - Work done together in 4 days.
Time taken to complete remaining work = Remaining work / Work done by Hemant in 1 day.
Calculation:
⇒ Work done by Hemant in 1 day = 1 / 7.
⇒ Work done by Irfan in 1 day = 1 / 19.
⇒ Work done by Hemant and Irfan together in 1 day = (1 / 7) + (1 / 19).
⇒ Work done by Hemant and Irfan together in 1 day = (19 + 7) / (7 × 19).
⇒ Work done by Hemant and Irfan together in 1 day = 26 / 133.
⇒ Work done by Hemant and Irfan together in 4 days = (26 / 133) × 4.
⇒ Work done by Hemant and Irfan together in 4 days = 104 / 133.
⇒ Work remaining = 1 - (104 / 133).
⇒ Work remaining = (133 - 104) / 133.
⇒ Work remaining = 29 / 133.
⇒ Time taken by Hemant to complete remaining work = (29 / 133) ÷ (1 / 7).
⇒ Time taken by Hemant to complete remaining work = (29 / 133) × 7.
⇒ Time taken by Hemant to complete remaining work = 203 / 133.
⇒ Time taken by Hemant to complete remaining work = 1 70 / 133.
⇒ Time taken by Hemant to complete remaining work = 1101911019
.
∴ The correct answer is 1101911019
.