Top 50 IPMAT Arithmetic Questions PDF with Video Solutions

In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

An alloy P has copper and zinc in the proportion of 5:2 (by weight), while another alloy Q has the same metals in the proportion of 3:4 (by weight). If these two alloys are mixed in the proportion of a:b (by weight), a new alloy R is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy S, formed by mixing the two alloys P and Q in the proportion of b:a (by weight), is

Fifty litres of a mixture of milk and water contains 30% water. This mixture is added to eighty litres of another mixture of milk and water that contains 20% water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25% water?

A fruit seller had a certain number of apples, bananas, and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of the apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was

Let a, b, c, d be positive integers such that a + b + c + d = 2023. If a : b = 2 : 5 and c : d = 5 : 2 then the maximum possible value of a + c is________.

The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams is INR 3600. The cost of a piece of jewellery of the same kind weighing 4 grams is

The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is

If $$\frac{a+b}{b+c} = \frac{c+d}{d+a}$$, which of the following statements is always true?

Three friends divided some apples in the ratio 3 : 5 : 7 among themselves. After consuming 16 apples they found that the remaining number of apples with them was equal to largest number of apples received by one of them at the beginning. Total number of apples these friends initially had was

In an election with only two contesting candidates, 15% of the voters did not turn up to vote, and 50 voters cast invalid votes. It is known that 44% of all the voters in the voting list voted for the winner. If the winner got 200 votes more than the other candidate, then the number of voters in the voting list is_________.

In a factory there are three types of machines b1, b2, and b3 which produces 20%, 15%, and 32% of the total products respectively. Further, machines b1, b2, and b3 which produces 3%, 7%, and 2% defective products respectively. Find the percentage of non-defective products?

A fruit seller has oranges, apples, and bananas in the ratio 3 : 6 : 7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is:

Guru and Chela walk around a circular path of 115 km in circumference, they start together from the same point. If they walk at speed of 4 and 5 kmph respectively, also they walk in the same direction, when will they meet?

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is

Two swimmers, Ankit and Bipul, start swimming from opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is-

A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.

Two friends run a 3 kilometer race along a circular course of length 300 meters.
If their speeds are in ratio 3:2, the number of times the winner passes the other is _____________.

A clock strikes 4 taking 9 seconds. In order to strike 12 at the same rate, the time taken is

When Geeta increases her speed from 12 km/hr to 20 km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is________km.

Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be______.

A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day it starts from point A, goes downstream for 1 hour, then upstream for 1 hour, and repeats this for four more times, that is, 5 upstream and 5 downstream journeys. Then the boat would be

In a 1000 meter race Rishi beats Koustab by 50 meters. In the same race, by what time margin Koustab beat Pandey who runs at 4 meter per second?

There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for the water tank (initially full) to become empty if T2 is opened while T1 is closed is ____________.

Ashok started a business with a certain investment. After few months, Bharat joined him investing half amount of Ashok’s initial investment. At the end of the first year, the total profit was divided between them in ratio 3:1. Bharat joined Ashok after

Arpita and Nikita, working together, can complete an assigned job in 12 days. If Arpita works initially to complete 40% of the job, and the remaining job is completed by Nikita alone, it takes 24 days to complete the job. The possible number of days that Nikita requires to complete the entire job, working alone, is

Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be ______.

Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is

The average spending of Lata Mangeshkar for the part of week from Monday to Saturday is Rs. 4200. She spent Rs. 1200 on Monday and Rs. 1500 on Sunday that week. The average spending for the part of week from Tuesday to Sunday that week is?

A class consists of 30 students. Each of them has registered for 5 courses. Each course instructor conducts an exam of 200 marks. The average percentage marks of all 30 students across all courses they have registered for is 80%. Two of them apply for revaluation in a course. If none of their marks reduce, and the average of all 30 students across all courses becomes 80.02%, the maximum possible increase in marks for either of the 2 students is

In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. Then m : n is

The height of nineteen people of comic book is in Arithmetic progression. The average height of them is 19 feet. If the tallest is 37 feet. Then what is the weight of the shortest?

Average stipend of summer internship of an institute is Rs. 20000 per month. Recently the institute announced increment of Rs. 2000 per month for all the students. The new average stipend of students will now be?

In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2,4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

Let 50 distinct positive integers be chosen such that the highest among them is 100 , and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50 . Then the maximum possible value of the sum of all the 50 integers is _________.

Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ____

A hotel has 459 managers. When the number of managers is increased by 36, the total daily expenditure on food increases by ₹81, but the average food expenditure per person decreases by ₹1. Find the hotel’s original daily expenditure on food.

The average marks of 6 students in a test are 64. All the students got different marks; one of the students obtained 70 marks, and all the other students scored 40 or above. The maximum possible difference between the second-highest and the second-lowest marks is

The average age of a group of 9 friends is 22 years. LAVGIR is the youngest and his age is 6 years, then what happened to be the average age of the family just before LAVGIR was born?

The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is

The average presence of employees of a company for yoga sessions in an office on Monday, Tuesday and Wednesday is thirty two and on the Wednesday, Thursday, Friday and Saturday is thirty. If the average number of employees on all the six days is twenty six then the number of employees who attended the sessions on Wednesday is?

If the difference between compound interest and simple interest for a certain amount of money invested for 3 years at an annual interest rate of 10% is INR 527, then the amount invested in INR is

Assume it is the beginning of the year today. Ankita will earn INR 10,000 at the end of the year, which she plans to invest in a bank deposit immediately at a fixed simple interest of 0.5% per annum. Her yearly income will increase by INR 10,000 every year, and the fixed simple interest offered by the bank on new deposits will also increase by 0.5% per annum every year. If Ankita continues to invest all her yearly income in new bank deposits at the end of each year, the total interest earned by her, in INR, in five years from today will be__________.

Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is

Bhavani invested an amount of Rs. 13900 divided in two different schemes, A and B at the simple interest rate of 14% per annum and 11% per annum respectively if the total amount of simple interest earned in two year be Rs. 3508, what was the amount invested in Scheme B?

Anindita invests a total of 1 lakh rupees distributed across three schemes, A, B and C, for a period of two years. These schemes offer an interest rate of 10%, 8% and 12% per annum, respectively, each compounded annually. If the initial investment amount in scheme A is 30000 rupees and the total interest earned from all three schemes during the first year is 10600 rupees, then the total interest earned, in rupees, from all three schemes for the second year is

Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 10% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150 . Then the number of apples purchased by Aruna is _________.

A shopkeeper reduces the price of a pen by 25% as a result of which the sales quantity increased by 20%. If the revenue made by the shopkeeper decreases by x%, then x is

One Trader calculates the percentage of profit on the buying price and another calculates on the selling price. When their selling prices are same, then the difference of their actual profit is Rs 85 and both claim to have made 20% profit. What is the selling price for each?