Question
A train approaches a tunnel a PQ. Inside the tunnel a
cat located at a point i.e., 7/16 of a distance PQ measured from the entrance P. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel P, the train catches the cat exactly at the entrance. If the cat moves to the exit Q, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order?Solution
Let the speed of train be ‘a’ and Speed of cat be ‘b’ and Train whistles at a point ‘T’, x km away from P, then First case: => a/b = x/(7k) Second case: => a/b = (x+16)/(9k) From both cases: => 9x = 7 (x+ 16 k) => 9x = 7x = 102 k => 2x = 102k => x/k = 56/1 => a/b = 56/(7x1) = 8/1
Determine the sum of the first 16 odd numbers.
A two-digit number has a sum of its digits equal to 12. Additionally, if 45 is subtracted from this number, the resulting number has its digits reversed...
A = (5/2) × B and C = (1/10) × A. If (A + B + C) = 255, then determine the value of (7C – B).
3245.34 + 923.5 + 23.5 =?
In a class, 1/3 of the students are girls and rest are boys. If 3/5 of the girls and 1/5 of the boys are absent, what part of the total number of studen...
On reversing its digits, a two-digit number becomes 78 less than 180% of the original number. Also, the difference between the digits is 2 (tens digit ...
The sum of the squares of three natural numbers is 342. These numbers are in the ratio of 3:5:2. Determine the difference between the largest and smalle...
When a number is increased by 20% then the number obtained is 72 less than thrice the original number. Find the original number.
This question is based on the following 3-digit numbers:
543, 769, 552, 342, 245
(Example: 697 – First digit = 6, second digit = 9, and ...
When a number is divided by 17, the remainder remains 6. Find the remainder obtained when the square of the same number is divided by 17.
Relevant for Exams:
