Ram and Shyam together can do a work in 8 days. Both of them began to work. After 3 days Ram fell ill. Shyam completed the remaining work in 15 days. In how many days can Ram complete the whole work?

Ram and Shyam together complete work in 8 days, so their combined rate is 1/8 per day. After 3 days, 3/8 work is done, leaving 5/8. Shyam completes 5/8 in 15 days, so Shyam's rate = (5/8)/15 = 1/24 per day. Ram's rate = Combined rate - Shyam's rate = 1/8 - 1/24 = 3/24 - 1/24 = 2/24 = 1/12 per day. Therefore, Ram alone completes the work in 12 days. Options A (17), C (15), and D (13) are incorrect.