AILET entrance exam Question Bank Solutions for Mathematics

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

A does 80% of work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same work in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be

Twenty women can do a piece of work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days, will 10 women complete it?

A and B can together finish work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days, A alone can finish the work?

A, B and C can do a piece of work in 20, 30 and 60 days, respectively. In how many days can A do the work, if he is assisted by B and C on every third day?

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for ₹ 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A, B and C can do a piece of work in 20, 24 and 30 days, respectively. They undertook to do the piece of work for ₹5400. They begin the work together but B left 2 days before the completion of work and C left 5 days before the completion of work. The share of A from the assured money is

A, B, and C get  ₹5400 for doing work in 36 days. A and C get ₹1880 for doing the same work in 20 days, which B and C get ₹3040 for doing the same work in 40 days. Find the amount received by C per day.

Pipes P and Q can fill a tank in 5 and 6 h respectively. Pipe R can empty it in 12 h. If all the three pipes are opened together, then the tank will be filled in :

Two pipes P and Q can fill a tank in 15 min and 20 min, respectively. Both the pipes are opened together but after 4 min, pipe P is turned off. What is the total time required to fill the tank?

15 men can do a work in 20 days. If there are 25 men, how many days will it take to complete the work?

Ram can do a work in 60 days and the same work Sohan can finish in 40 days. If both of them work together, then in how many days will the work be over?

Sanju has two watches with a 12-hour cycle. One of these watches gains one minute a day and the other loses 1 and `1/2` minutes per day. If Sanju sets both the watches at the correct time, how long will it be before they again show the correct time together?

How many three-digit positive integers exist that when divided by 6 leave a reminder of 4?

A positive integer is written on each face of a cube. Each vertex is then assigned the product of the numbers written on the three faces intersecting the vertex. The sum of the numbers assigned to all the vertices is equal to 1001. Find the sum of the numbers written on the faces of the cube.

Solve the following question and mark the best possible option.
If x, y, z are positive real numbers, such that x + y + z = 25, then the maximum value of `1/x + 1/y + 1/z` is

Solve the following question and mark the best possible option.
Let A = { 3, 6, 9, 12, ......., 696, 699} & B = {7, 14, 21, .........., 287, 294}
Find no. of ordered pairs of (a, b) such that a ∈ A, b ∈ B, a ≠ b & a + b is odd.

Solve the following question and mark the best possible option.
If a, b, c > 0, then find the minimum value of (a + b + c)`(1/(a + b) + 1/(b + c) + 1/(c + a))`.