Management Aptitude Test 2014 Paper

(b) Let the time taken by Ram to finish the race = t min Case I Ram gives Shyam a start of 200 m and beats him by 30 s, i.e., $\frac{1}{2}$ min. ∴ Speed of Ram = $\frac{2000}{t}$and, speed of Shyam = $\frac{1800}{t+\frac{1}{2}}$ Case II Here, Ram gives Shyam a start of 3 min and losses to Shyam by 1000 m. ∴ Time taken by Shyam - Time taken by Ram = 3 m $\frac{2000}{\frac{1800}{t+\frac{1}{2}}}-\frac{1000}{\frac{2000}{t}}$ = 3 ⇒ $\frac{2000}{\frac{1800\times2}{2t+1}}-\frac{t}{2}$ = 3 ⇒ $\frac{2000\times(2t+1)}{1800\times2}-\frac{t}{2}$ = 3⇒ $\frac{5}{9}(2t+1)-\frac{t}{2}$= 3⇒ $\frac{10(2t+1)-9t}{18}$ = 3 ⇒ 20t + 10 - 9t = 18 x 3 ⇒ 11t = 54 - 10 ∴ t = $\frac{44}{10}$ = 4min So, time taken by Ram to finish the race is 4 min. Again, speed of Shyam = $\frac{1800}{t+\frac{1}{2}}$ ⇒ $\frac{1800}{4+\frac{1}{2}}$ = $\frac{1800}{8+1}\times2$ = 400 m/min So, to cover 2000 m Shyam will take 5 min.