A man walks a certain distance in certain time, if he had gone 3 km an hour faster, he would have taken 1 hour less than the schedule time. If he had gone 2 km an hour slower, he would have been one hour longer on the road. The distance (in km) is

Let ideal speed of man = $$s$$ km/hr and ideal time = $$t$$ hours

=> Distance = $$d=st$$ ------------(i)

According to ques, => $$d=(s+3)(t-1)$$

=> $$d=st-s+3t-3$$

Thus, using equation (i), => $$3t-s=3$$ ------------(ii)

Also, $$d=(s-2)(t+1)$$

=> $$d=st+s-2t-2$$

=> $$-2t+s=2$$ ------------(iii)

Adding equations (ii) and (iii), we get :

=> $$3t-2t=3+2$$

=> $$t=5$$

Substituting above value in equation (ii), => $$s=3(5)-3=15-3=12$$

$$\therefore$$ Distance = $$12\times5=60$$ km

=> Ans - (D)