Let r denotes the more time (in hrs) required for R than for Q to overtake P after it has traveled for the time,let it be denoted by t (in hrs).Hence from above data we get following relation,t*a = (t + p)*(a + b) = (t + p + r)*(a + 2*b) [= equal distance covered by P, Q & R]From above relation we get,t*a = (t + p)*(a + b) …… (1a)t*a = (t + p + r)*(a + 2*b) …… (1b)From (1a) we get,t*a = t*a + t*b + p*(a + b)or - t*b = p*(a + b) …… (1c)From (1b) & (1c) we get,t*a = (t + p + r)*(a + 2*b)or (p + r)*(a + 2*b) = - 2*t*bor p*(a + 2*b) + r*(a + 2*b) = 2*p*(a + b)or r*(a + 2*b) = p*aor r = p*a/(a + 2*b) (hrs) [Ans]

Unable to approach image.png 39.06 KB

Unable to approach image.png 39.06 KB