At the same instant, train A leaves station P towards station Q and train B leaves station Q towards station P, each moving at its own constant speed along the same straight track. After they cross each other, A takes exactly 4 hours to reach Q, and B takes exactly 9 hours to reach P. If the speed of B is 40 km/h, what is the distance (in km) between P and Q? Enter the answer as an integer. - -

A teacher distributes 15 identical pens among 4 students A, B, C, D such that every student receives at least 2 pens and no student receives more than 6 pens. In how many ways can this be done?

A committee of 5 is to be formed from a pool of 6 men and 5 women such that the committee has strictly more women than men. A specific man M and a specific woman W refuse to serve together. In how many ways can such a committee be formed?

A string of length 6 is formed using the digits {1, 2, 3, 4, 5, 6, 7, 8, 9} (repetition allowed). The string must contain exactly two 5s, and the two 5s must not be adjacent. Find the total number of such strings.

A person starts a journey at a constant speed and plans to complete it in 6 hours. After travelling for some time, he stops for 20 minutes and then increases his speed by 5 km/h to reach exactly on time. Had he stopped for 10 minutes more at the same point, he would have had to increase his original speed by 8 km/h to reach exactly on time. Find his original speed, in km/h.

A 5 - digit number is formed using 5 distinct digits chosen from {1, 2, 3, 4, 5, 6, 7} in such a way that the digits, read from left to right, are in strictly increasing order. The number of such 5 - digit numbers that are divisible by 4 is

A rider starts from city A to city B at a constant speed and is scheduled to reach B on time without any halt. After covering one - third of the distance, the rider halts for 24 minutes and then increases the speed by 20%, reaching B 9 minutes late. On another day, after covering one - third of the same distance at the same initial speed, the rider halts for 18 minutes and then increases the speed by 25%, reaching B exactly on time. What is the scheduled travel time, in minutes?

A container has 80 litres of pure milk. In each operation, a fixed quantity of x litres is drawn out and replaced with water. After two such operations, the quantity of milk left in the container is exactly 45 litres. Counting the very first operation as operation 1, after how many such operations will the quantity of milk in the container first become less than 20 litres?

A three - digit number N has the property that the number obtained by reversing its digits is exactly 198 more than N. The sum of the digits of N is 14. How many such three - digit numbers N exist?

A fruit vendor has 212 fruits consisting only of apples, mangoes and oranges. The numbers of apples and mangoes are in the ratio 7: 3. She sells 50 apples, 18 mangoes and exactly half of the oranges. After this, the ratio of unsold apples to unsold oranges is 4: 3. Find the total number of unsold fruits.

A cafeteria offers 4 types of bread, 5 types of fillings, 4 types of sauces and an optional cheese slice. A sandwich must have exactly one type of bread, either one or two fillings, and at least one sauce. Cheese may or may not be added. How many different sandwiches have an odd number of add - ons, where add - ons include selected fillings, selected sauces and cheese if selected?

A piece of work can be completed by A alone in 12 days and by B alone in 18 days. They decide to work in the following 3 - day cycle: A alone on day 1, B alone on day 2, and both together on day 3. However, on every joint day, each of A and B works at only 80% of his usual efficiency. If they keep repeating this 3 - day cycle, the total number of days required to finish the work is:

TITA} A trader marks his goods $40$ above cost price and offers a discount of $d$ on the marked price. He also uses a faulty balance that displays $1000$ g but actually delivers only $800$ g of the goods. If his overall profit is exactly $40$ of the actual cost price of the goods he physically delivers, find the value of $d$.

MCQ} The number of positive integers $n \le 600$ such that $n$ is divisible by exactly two of the three numbers $4$, $6$, and $9$ is:

A vessel contains 80 litres of pure milk. The following operations are performed in sequence on the vessel: - 8 litres of the contents are drawn out and replaced by an equal quantity of water. - Then 16 litres of the resulting mixture are drawn out and replaced by an equal quantity of water. - Finally, 20 litres of the resulting mixture are drawn out and replaced by an equal quantity of water. After all three operations, what is the percentage of milk in the vessel? Enter the answer as an integer (the answer is exactly an integer). - -