Question
What will be the remainder which 5382 + 53 is
divided by 54?Solution
(53)82 + 53 = 53[(53)81 + 1] Clearly (an + 1) is always divisible by (a + 1) which n is odd. So (53)81 + 1 is divisible by (53 + 1) 54, Thus remainder is zero.
- Two cars, βXβ and βYβ, started from towns βMβ and βNβ towards each other at the same time. When they met after 6 hours, car βYβ had tra...
A and B are travelling towards each other with a speed of 30 km/hr and 40 km/hr. If they started at same time and A covered 22 km less distance than B b...
A,B and C run around a Circular track starting from the same point simultaneously and in the same direction at the speed of 16 kmph, 24 kmph and 32 kmph...
A passenger train takes 3 hours less for a journey of 180 km, if its speed is increased by 2 km/hour from its usual speed. Find the usual speed of the t...
The distance between two stations A and B is 900 km. A train starts from A and moves towards B at an average speed of 30 km/hr. Another train starts fr...
Ajay and Vishal left the place βXβ with different speeds which are in the ratio 5:3 respectively. Ajay left the place 36 seconds after Vishal. If af...
Tarun takes 1hr 30 min in walking to a certain place and riding back. He would have gained 40 min by riding both ways. How long would he take to walk bo...
A train 120 m long crosses another train 150 m long, coming from the opposite direction, in 10 seconds. If the speed of the first train is 54 km/h, find...
A man running with the speed of 65 km/hr covers a certain distance in βxβ hours. If the same distance can be travelled with a speed of 70 km/h in (x...
'A' starts a journey and covers the first half of the total distance at a speed of 15 km/hr. Then, he travels half of the remaining distance at 5 km/hr ...