Arithmetic: percentage, ratio, averages, time & work: practice set 3

The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?

X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?

Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had team Y’s average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by team X?

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z.

1. Value-I: Runs scored by X
2. Value-II: Runs scored by Y
3. Value-III: Runs scored by Z

Which one of the following is correct?

A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?

A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct?

Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below:

1. 1.Z purchased 8 notebooks more than X did.
2. 2.P and Q together purchased 21 notebooks.
3. 3.Q purchased 5 notebooks less than P did.
4. 4.X and Y together purchased 28 notebooks.
5. 5.P purchased 5 notebooks more than X did.

If each notebook is priced ₹40, then what is the total cost of all the notebooks?

From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0.15n for any n. On which date in the year 2021 are the prices of these two fuels equal?

There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.

Consider the following statements:

1. 1.The average score of Class-B will definitely decrease.
2. 2.The average score of Class-A will definitely increase.

Which of the above statements is/are correct?

If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?

A sum of ₹ 2,500 is distributed among X, Y and Z in the ratio 1/2: 3/4: 5/6. What is the difference between the maximum share and the minimum share?

A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?

Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent ₹ 1300 and Rajesh spent ₹ 1500. If each racket costs three times a ball does, then what is the price of a racket?

The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are

Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?

Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal’s position if he agreed?

The average rainfall in a city for the first four days was recorded to be 0.40 inch. The rainfall on the last two days was in the ratio of 4: 3. The average of six days was 0.50 inch. What was the rainfall on the fifth day?

In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

W can do 25% of a work in 30 days, X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?