Chintu works at a soft drink company and was arranging some particular number of cylindrical aluminium soft drink cans in a square box but the box became full and there were 14 cans remaining to be put in. Then, he started arranging all Cans in a rectangular box where he could arrange 8 cans more along the length than the breadth after putting all the cans in the rectangular box. He found out that there was still space left for another 9 cans. What is the number of cans Chintu had if it is known that the number of cans were more than 10 and no can was put on top of another can?
In a square box the number of cans arranged along the length and breadth would be same.
In case of rectangular box, lets assume that number of cans along breadth is x then number of boxes along the length would be x+6
Total number of cans the rectangular box can take = x*(x+8)
Total number of cans Chintu was able to put in the rectangular box (as some empty space was remaining ) = x*(x+8) - 9 --- (i)
Given that the number of cans are more than 10, hence 2 & 3 cans along the length are ruled out
Lets try with 4 cans along length of square box, total cans in box would be 16
Total number of cans which Chintu has = 16+14 = 30 ---- (ii)
(i = (ii)
x*(x+8) - 9 = 30
=> x^2 + 8x = 39
Trying to solve we realize that there is no such whole number which x can take
Lets try with 5 cans along length of square box, total cans in box would be 25
Total number of cans which Chintu has = 25+14 = 39 ---- (ii)
(i = (ii)
x*(x+8) - 9 = 39
=> x^2 + 8x = 48
Solving we get x = 4
So total number of cans which Chintu had = x*(x+8) - 9 = 4(4+8) - 9 = 39
Fatafat express train traveling at 90 kmph crosses a platform in 30 seconds and a person standing on the platform in 18 seconds. What is the length of the platform in meters?
Rohit and Virat, working together, can complete an assigned task in 20 days. If Rohit worked alone and completes half the task and then Virat takes over and completes the remaining half, then the task gets completed in 45 days. How long will Rohit take to complete the task if he worked alone? Assume that Rohit is more efficient than Virat.
Let Rohit take 'x' days to complete the task if he worked alone.
Let Virat take 'y' days to complete the task if she worked alone.
Given that They will complete the task in 20 days, if they worked together.
In 1 day, Rohit will complete 1/x of the task.
In 1 day, Virat will complete 1/y of the task.
Together, in 1 day they will complete 120 of the task.
Therefore,1/x + 1/y = 1/20 .... (1)
As per question if Rohit worked alone and completed half the work and then Virat takes over and completes the second half, the task will be completed in 45 days.
Rohit will complete half the task in x/2 days.
Virat will complete half the task in y/2 days.
∴ x/2 + y/2 = 45
Or, x + y = 90 or x = 90 - y .... (2)
Solving 1 and 2 we get
y^2 - 90y + 1800 = 0
=> y 30 or 60
The question clearly states that Rohit is more efficient than Virat. Therefore, Rohit will take lesser time than Virat.
So Rohit will take 30 days
Out of 123 persons, the first person will shake hand with 122 persons.
The second person will shake hand with 121 persons (because he has already shaken hand with first person).
The third person will shake hand with 120 persons and so on. The second last person shakes hand with only one person. And last will shake hand with none
(because he has already shaken hand with all persons).
In order to find the total number of handshakes you have to add all the natural numbers from 1 to 122 i.e. ∑ 122.
∑122 = 123 x 122/2 = = 7503 handshakes.
The profit earned by selling a chocolate for Rs 900 is double the loss incurred when the same chocolate is sold for Rs.490. At what price should the chocolate be sold to make 25% profit?