AILET entrance exam Question Bank Solutions for Mathematics

At the beginning of a partnership business, the capital of B was `3/2` times that of A. After 8 months B withdrew `1/2` of his capital and after 10 months A withdrew `1/4`of his capital. At the end of the year, if the profit incurred is ₹53000 find the amount received by A.

Two partners invest ₹125000 and ₹85000, respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets ₹600 more than the other, find the total profit made in the business.

In a mixture of 60L, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is

4 L is drawn from a container full of milk and then is filled with water. This operation is performed three more times. The ratio of the quantity of milk left in the container and that of water is 16 : 65. How much milk did the container hold initially?

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 L of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7: 9. How many litres of liquid A was contained by the can initially?

Tea worth ₹126 per kg and ₹135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth ₹153 per kg, the price of the third variety per kg will be

How many kilograms of sugar costing ₹9 per kg must be mixed with 27 kg of sugar costing ₹7 per kg so that there may be a gain of 10% by selling the mixture at ₹9.24 per kg?

Find the ratio in which rice at ₹7.20 per kg, be mixed with rice at ₹5.70 per kg to produce a mixture worth ₹6.30 per kg.

Simran started a software business by investing ₹50000. After six months, Nanda joined her with a capital of ₹80000. After 3 years, they earned a profit of ₹24500. What was Simran's share in the profit?

A, B, C subscribe ₹50000 for a business. A subscribes ₹4000 more than B and B ₹5000 more than C. Out of a total profit of ₹35000, A receives

The average age of three friends A, B, and C is 7 years. Five years later, the average age of A and C will be 1½ years more than B's age then. How old will B be 10 years hence (in years)?

Choose the most appropriate option:
A library has an average of 510 VIS1tors on Sunday and 240 on the other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is 

Solve the following question and mark the best possible option.
In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation and if the weight is taken in whole numbers so that all the above conditions are satisfied, what is the average of different probable weights of Arun?

Solve the following question and mark the best possible option.
The average age (in years) of a class is twice the number of students in the class. A student, X leaves the class and the average age is still twice the number of students in the class. Now another student Y leaves the class and the average is still twice the number of students in the class. If the ratio of the ages of X and Y is 19: 17, then find the average age of the class, if one more student Z of age 16 years leaves the class.

Solve the following question and mark the best possible option.
The average marks scored by two groups X and Y of students are 70 and 75 respectively. Four students are moved from group Y to group X, thereby interchanging the average marks of the two groups. Find the total number of students in two groups put together, if the average marks scored by the four students who moved are 85.

When numbers are associated with weights, then obtanied mean is said to be

Successive averages which are computed  for a sequence of days/months/years at a time is called

The average price of 10 pens is Rs. 12 while the average price of 8 of these pens is Rs. 11.75. Of the remaining two pens, if the price of one pen is 60% more than the price of the other, what is the price of each of these two pens?

The ratio between the present ages of Anu and Balbir is 5: 3, respectively. The ratio between Anu's age 4 years ago and Balbir's 4 years hence is 1: 1. What is the ratio between Anu's age 4 years hence and Balbir's age 4 years ago?