Let W be the workNo. of days taken by a man alone to complete the work be x days &no. of days taken by a boy alone to complete the work be y daysTherefore one days work by a man = W/xand one days work by a boy = W/y CASE 1one days work of 8 men and 12 boys = 8 W/x+12 W/yand ten days of work by 8 men and 12 boys = Wtherefore, 10 [8 W/x +12 W/y]=W80 W/x+120 W/y = w80/x + 120/y = 1............(1)

CASE 2following the same steps according to the given condition we get the 2 n d equation as84/x+112/y = 1.............. (2)

take 1/x =u and 1/y=v80 u+ 120 v=1...............(3)84 u+ 112 v=1...............(4)

Multiply eq(3) by 21 and eq(4) by 201680 u+2520 v = 21........ (5)1680 u+2240 v = 20.........(6) solving we will get v = 1/280substituting value of v in (3)80 u +120 *1/280 =180 u= 1-3/780 u= 7-3/7 {l c m}80 u =4/7u= 4/7*80u= 1/140

when v = 1/2801/y=1/280therefore y = 280

when u = 1/1401/x = 1/140therefore x = 40

therefore no.of days taken by a man alone to complete the work = x days = 140 days &no. of days taken by a boy alone to complete the work = y days = 280 days

(2) is correct option