Sushant runs 4 times as fast as Sulleman. If Sushant gives Sulleman a start of 60 m, how far must the goal on the race course be so that Sushant and Sulleman reach it at the same time?
Ratio of the speeds of Sushant and Sulleman = 4:1.
In a race of 4 m, Sushant gains 3 m over Sulleman.
60 meters will be gained by Sushant in race of (4/3 × 60 = 80 m).
Thus, Winning post must be at a distance of 80 m from the starting point.
In the same time, Amar covers 80 m, Akbar covers (80 – 5) = 75 m, and Anthony covers (80 – 20) = 60 m.
If the race is between Akbar and Anthony only, applying unitary method, when Akbar runs 75 m, Anthony runs 60 m.
Hence, when Akbar runs 80 m, Anthony runs (60/75 × 80 = 64)
A red color thread is 37 cm long. It is cut into 3 pieces. The longest piece is 3 times as long as the middle-sized piece & the shortest piece is 19 cm shorter than the longest piece. Find the length of the shortest piece
(in cm).
Now we can see that whatever the value of ‘a’, 26a + 13 will always give an integral value.
So, it now depends upon 8/a only
=> a can have any integral value, which is a factor of 9.
The integers, which will satisfy this condition are ±1, ±3, ±9. Thus, in total,a can take 6 values.