in the given options only 71 and 73 are primes.
The 10% discount is offered on all the items. Let us first calculate the selling price of each.
Cost Price
Discount
Selling price
450
45
405
520
52
468
250
25
225
Total
122
1098
The total selling price is Rs. 1098 which is greater than Rs. 1000, so Dilshan will get an additional discount of 5%.
5% of 1098 = Rs. 54.90
Total Discount = 122 + 54.90 = Rs. 176.90
(7:00 am Rajdhani) Meeting point
30 km x km
Suratkal
Rajdhani (5:00 am at 15 kmph)
Shatabadi (7:00 am at 20 kmph)
Rajdhani train starts at 5:00 am and Shatabadi train starts at 7:00 am. So by the time Shatabadi starts, Rajdhani has already covered 2 hours worth distance.
Rajdhani train is travelling at the speed of 15 kmph so in 2 hours it has covered 30 km.
Let us assume the trains meet at the distance x km from the point where Rajdhani has reached at 7:00 am. Also the time taken to reach the meeting point by both trains should be same.
Let us calculate the time taken by both trains.
Rajdhani has covered distance x km at the speed of 15 kmph.
Time taken = DistanceSpeed = x15 …..(1)
Shatabadi has covered distance (x+30) km at the speed of 20 kmph.
Time taken = DistanceSpeed = x+3020 …..(2)
Time taken should be same in both the cases. Therefore,
x15 = x+3020 ; which gives x = 90 km.
Shatabadi has covered the total distance of (x+30) 120 km at the speed 20 kmph. Time taken is (12020) 6 hours. It starts at 7:00 am and after 6 hours the time will be 1:00 pm.
Alternatively,
Rajdhani has covered 30 km distance in the time between 5:00 am and 7:00 am. Both the trains are travelling in the same direction so the relative speed for both the trains will be (20 -15) 5 kmph. The difference between the distances that Rajdhani train has covered in two hours is the distance to be covered in order to meet.
Time taken = Difference in distancerelative speed = 305 = 6 hours.
Shatabadi starts at 7:00 am and after 6 hours the time will be 1:00 pm.
Note: We are taking 7:00 am as the starting time and not 5:00 am because at 5:00 am only one train is moving. The trains will meet only after the second train starts moving.
let cp be 100, when price decreased by 10% then sp=90. Now sales increased by 20%, ie, 90+20%of90=108. so cp=100, sp=108, gain=8, gain%=gain*100/cp=8%increase
Sum of digits must be divisible by 3, so Sum = 28+* so least number in place of * can be 2