Find the sum of all four-digit numbers N whose sum of digits is equal to 2010 – N.
N has to be greater than 2010 – 28 = 1982 because maximum sum of digits less than 2010 is 1 + 9 + 9 + 9 i.e. 28. Now checking for all the decades there are only two possible values of N i.e. 1986 and 2004. So the required sum is 3990.
You have two ropes coated in an oil to help them burn. Each rope will take exactly 1 hour to burn all the way through. However, the ropes do not burn at constant rates—there are spots where they burn a little faster and spots where they burn a little slower, but it always takes 1 hour to finish the job.
With a lighter to ignite the ropes, how can you measure exactly 45 minutes?
Because the ropes burn at inconsistent rates, you can’t simply measure 75 percent of the way down one rope and call that 45 minutes. The rope might burn slightly faster or slower in that last 25 percent. However, if you light one of the ropes on fire at both ends at the same time, it will burn up in 30 minutes, even if one side burns faster than the other. So here’s what you do: Light one of the ropes on fire on both ends and light the second rope on one end at the same time. When the first rope burns out, 30 minutes have elapsed. At that exact moment, you light the unlit end of the second rope. Because 30 minutes of the second rope have already been used up, 30 more remain (though this does not necessarily mean that half of the rope’s length has been burned, it could be more or less). Lighting the other end at the moment the first rope burns up will cause the remaining part of the second rope to burn up in 15 minutes. Once the second rope has been consumed by the flames, exactly 45 minutes have passed.
Munish and Amit play chess with strangers on internet. Munish won 3 of his first 5 games while Amit won 7 out of his first 8 game. From now on if they play similar number of games then minimum how many games they must play such that the ratio of games won to the total number of games for Munish become more than Amit?
A horse stands at the corner of a chessboard, a white square. With each jump, the horse can move either two squares horizontally and one vertically or two vertically and one horizontally (like a knight moves). The horse earns two carrots every time it lands on a black square, but it must pay a carrot in rent to rabbit who owns the chessboard for every move it makes. When the horse reaches the square on which it began, it can leave. What is the maximum number of carrots the horse can earn without touching any square more than twice?
The horse must alternate white and black squares, and it ends on the same square where it started. Thus it lands on the same number of black squares (b) as white squares (w). Thus, its net earnings will be 2b − (b + w) = b − w = 0 carrots, regardless of its path.
Arun and Varun ran a 500 m race from point P to point Q. Arun won by 50 m. So Varun challenged him for another race. But this time Arun started from a point R, 20 m before P (i.e. 20 m further away from Q), while Varun started from a point S, 30 m after P. What will be the result?
1. Arun beat Varun by 2m
2. Both reached Q at same time.
3. Varun won the race
4. Arun beat Varun by more than 10 meters
Find the missing character from the given alternatives.
1. 10
2. 12
3. 9
4, 8
Order alphabets as A=1, B=2, C=3,………Y=25, Z=26. Then, M-J = 13-10 = 3, Y-O = 25-15 = 10, R-C = 18-3 = 15. So, the missing number = K-B = 16-7= 9.
Two trains Sapt Kranti Express and Sampurna Kranti Express start from stations Ambala and Bhatinda towards each other at speeds of 50 km/hr and30 km/hr respectively. When they meet, it is found that the slower train has travelled 60 km less than the faster train. What is the distance (in km) between the two stations Ambala and Bhatinda ?
1. 240km
2. 220km
3. 180km
4. 300km
The sum of the incomes of Anna and Banna is more than that of Canna and Danna together. The sum of the Incomes of Anna and Canna is the same as that of Banna and Danna taken together. Moreover, Anna earns half as much as the sum of the incomes of Banna and Danna?
Whose income is the highest?
Lets take Anna, Banna, Canna and Danna to be A, B, C and D respectively. We have (A+B) > (C+D) (1) (A+C) = (B+D) (2) A = 1/2 (B+D) (3) Putting the value of A in (2) statement we get A=C Since (A+B) > (C+D) and A = C so B > D Thus from (3) we get B > A ans so B > C. Thus, clearly B has the highest income.
