Skip to content
← Applied Mathematics

Applied Mathematics · Class 11 Commerce

Ch 2Numerical Applications — Class 11 Applied Mathematics, concept-first.

This concept map shows how the chapter fits together. Numerical and quantitative aptitude gathers several everyday problem types: averages, mensuration of 2-D and 3-D shapes, calendars and clocks, time, work and distance, and seating arrangements (linear and circular).

70

Q&A

6

Concepts

Not available

Exam weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Introduction

You've been solving problems your whole life. When you see a new type of question, you first figure out what it's asking, then decide which tools to use, then carry out the steps.

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

Concept Map

This concept map shows how the chapter fits together. Numerical and quantitative aptitude gathers several everyday problem types: averages, mensuration of 2-D and 3-D shapes, calendars and clocks, tim…

2.1

Introduction

Numbers are not just abstract symbols — they are the language of measurement, comparison, and decision-making in everyday life.

2.2

Average

17 Q

The average is the single value that best represents a set of data — the one number you'd use if you had to pick one.

+Worked Examplesi5 questions
  1. Example 1The average monthly savings of a company was Rs. 12 Lakh for the first 3 months, Rs. 12.5 Lakh for the next 4 months and Rs. 31.2 Lakh durin…Free
  2. Example 2A school follows the following criterion for grading a student for annual result: | ASSESSMENT | WEIGHTAGE | |---|---| | Homework | 25% | |…Free
  3. Example 3The average of 4 positive integers is 39. The highest integer is 73 and the lowest integer is 19. The difference between the remaining two i…Preview
  4. Example 4Five years ago, average age of a family of five was 32 years. The family includes Mrs. and Mr. Rai, their son, daughter and daughter in law.…Preview
  5. Example 5An insect starts from a point A and covers distance AB in 4 seconds. Then covers distance BC in 7 seconds, distance CD in 5 seconds and dist…Preview
+Exercise 2.1i12 questions
  1. Q1There are 44 boys and 36 girls in a class. The Average marks of boys are 40 and that of girls is 38. Find the average marks of the class?Free
  2. Q2The average of five numbers is 87. If one of the numbers is excluded, then the average gets decreased by 5. Find the excluded number.Free
  3. Q3A nursery is closed on Sunday. The average plants sold in the remaining six days of a week is 156 plants and the average sale from Monday to…Free
  4. Q4The average of five consecutive numbers is 125. Find the product of the number at the extreme positions.Preview
  5. Q5Under MNREGA Schema 1000 new labourers are enrolled in Delhi. Earlier they were getting Rs 200 as daily wages, but now the authorities have…Preview
  6. Q6The mean of 35 observations was found to be 98.6. But later, it was found that 72 was misread as 27. Find the correct mean.Preview
  7. Q7The average annual PF contribution of certain number of defence officers is Rs 28560 and that of other officers is Rs 22500. The number of d…Preview
  8. Q85 years ago, the average age of the 3 children of Mr. Pandey was 8 years. A new baby is born in the family now. Find the present average age…Preview
  9. Q9In a restaurant 35 visitors can have lunch at a time. If the number of visitors increases by 7, then the expense of the restaurant on food i…Preview
  10. Q10The average of runs of Virat Kohli, the famous cricket player, of last 10 innings were 72. How many runs he must make in 11th inning to incr…Preview
  11. Q11An ant is moving around a circular path of radius 3.5 cm and takes 3 seconds to complete 1 revolution. Find the average speed and average ve…Preview
  12. Q12Sara walks 7.2 km in one and half hour and 3.5 km in 2 hours in the same direction. What is the Sara's average speed for the whole journey?Preview
2.3

Clock and Calendar

17 Q

Time is the most universal measure we use, yet its units — seconds, minutes, hours — are entirely human inventions.

+Worked Examplesi5 questions
  1. Example 6What would be the time four and a half hour before 2.15 pm?Free
  2. Example 7At what time between 4'o clock and 5'o clock, will the hands of a clock make an angle of $20°$?Free
  3. Example 8At what time between 3'o clock and 4'o clock will the hands of a clock collide?Preview
  4. Example 9Find the angle between the hands of clock when it struck 15 minutes past 7?Preview
  5. Example 10If 30th March 2020 was Monday. What would be the day after 61 days?Preview
+Exercise 2.2i12 questions
  1. Q1If today is a Tuesday, what will be the day on 7706th day?Free
  2. Q2Find the total number of days from 26th January 2008 to 15 May 2008?Free
  3. Q3If the second day of April month is a Friday, then find the last day of the next month?Free
  4. Q4Workout for the day of week on the given date: (1) 15th August 1947 (2) 22nd November 2025 (3) 21st September 2080 (4) 18th October 2100Preview
  5. Q5A local train from Mumbai leaves every 40 minutes from the station. When inquired by a passenger, the help desk executive informed that the…Preview
  6. Q6Pranil works in an electronics goods shop and the shop has offered 30% discount on MRP on all the goods in the month of October. On top of i…Preview
  7. Q7a) In a day, how many times is a straight angle formed between minute and hour hands? b) In a day, how many times is a right angle formed be…Preview
  8. Q8Find the angle between the minute hand and the hour hand at 7:40 pm?Preview
  9. Q9By 20 minutes past 5, how many degrees has the hour hand has turned through?Preview
  10. Q10At what time between 3'o clock and 4'o clock are the hands of a clock three degrees apart?Preview
  11. Q11Indian government has announced a complete lockdown for entire country from the Midnight of 25th March 2020 till the midnight of 14th April…Preview
  12. Q12India is 9 hours and 30 minutes ahead of Ottawa ON, Canada. What is time in Canada when it is 1:25 am in India?Preview
2.4

Time, Work and Distance

13 Q

Time, work, and distance are linked by a single idea: the rate at which something happens. When a person works, their output per unit time is a rate; when a vehicle moves, its speed is a rate.

+Worked Examplesi3 questions
  1. Example 11Speeds of two cars, A and B is in the ratio $\dfrac{Speed\ of\ car\ A}{Speed\ of\ car\ B} = \dfrac{x}{y}$. Find the relation between the tim…Free
  2. Example 12Reena completes her canvas painting in 4 days. Mihir finish the same canvas painting in 5 days. If they both work together find out the numb…Preview
  3. Example 13Pipe A can fill a tank in 20 hours. But due to a leakage it is taking thrice the time to fill the tank. If the tank is full, how long will i…Preview
+Exercise 2.3i10 questions
  1. Q1Navya is twice as efficient as Nitti. If they take 10 days to finish a certain job together. How much time will they take individually to fi…Free
  2. Q2A piece of work is finished in 30 days by A. Since C is thrice as good as A and A is twice as good as B. If A, B, C work together, then how…Free
  3. Q3X can do a piece of work in 60 days, whereas Y can do the same work in 40 days. Both started the work together, but X left after 10 days bef…Free
  4. Q4A train is running at 7/11 of its own speed due to fog and reached a place in 44 hours. What was the original time taken by the train if it…Preview
  5. Q5a) The signal poles on a railroad are placed 100 m apart, how many poles will be passed by a train in 8 hours if the speed of the train is 4…Preview
  6. Q6100 persons begin to work together on a project which was expected to be completed in 40 days. But after few days 40 persons left. As a resu…Preview
  7. Q7The efficiency of x, y, z are in ratio of 3:2:6 to finish a task. If they work together, they can finish it in 2 hours; find the time taken…Preview
  8. Q8A is three times as efficient as B. Also, A takes 30 days less than B for doing a piece of work. Find the time taken by them if they work a)…Preview
  9. Q9Machine P is 40% more efficient than Machine Q. Machine P can make 100 bags alone in 30 hours. Find the time taken to complete the order if…Preview
  10. Q10A Corporate firm is running in loss, they had categorized their employees into two teams, Team A and Team B. The firm has funds to pay Team…Preview
2.5

Mensuration

Mensuration is the branch of mathematics that deals with measuring lengths, areas, and volumes of geometric shapes.

+Exercise 2.4i15 questions
  1. Q1A cylindrical tank of base diameter 16 m and height 6 m requires a non-porous lining on its circular base and curved walls. The lining of th…Free
  2. Q2The area of a rectangular field is 104000 $m^2$. This rectangular area has been drawn on a map to the scale of 1cm to 100 m. The length is s…Free
  3. Q3A rope by which a mare is tied at a centre of the circular field is decreased from 23m to 11 m. a) What is the decrease in area more will be…Free
  4. Q4A cone is surmounted on a hemisphere as shown here. The radius of the solid formed is 6 cm and its height is 21 cm. Find: i) Curved surface…Preview
  5. Q5Find the area of the greatest circle which can be inscribed in a square whose perimeter is 180 cm?Preview
  6. Q6The length and breadth of rectangle are increased by 30% and decreased by 20% respectively. Determine the percentage of increase or decrease…Preview
  7. Q7Dimensions of the cuboidal hall are 10 m x 12 m x 15 m. Find the length of the longest rod that can be fitted into the hall.Preview
  8. Q8A rectangular hall is to be carpeted with a vinyl flooring sheet 25 cm wide, available at the rate of Rs. 22.60 per metre square. If the are…Preview
  9. Q9Area of circle is numerically equal to twice of its circumference. Find the diameter of the circle.Preview
  10. Q10The following isosceles right-angled triangles represent the monthly expenditures of two law firms X and Y. If the monthly expenditure of fi…Preview
  11. Q11Shakuntala designed a toy car. Help her to find the area of the given below. [Figure: a composite car-shaped figure made of a central rectan…Preview
  12. Q12A circular park 120 m in diameter has a path of 10m wide all around outside, which is to be gravelled. The MCD received tenders from three c…Preview
  13. Q13A swimming pool 36 m wide and 27 m long is 3m deep on the shallow end and 4 m deep at the deeper end. Find the capacity of the pool (in litr…Preview
  14. Q14Nishant owns a house of dimensions 10 feet x 8 feet x 9 feet. His house has two entry doors on the opposite sides, of dimension 7 feet by 3…Preview
  15. Q15A cubical gold block of dimensions of 9cm x 11cm x 12 cm is melted and recasted into spherical balls of radius 3 mm. Find the number of sphe…Preview
2.6

Seating Arrangements

8 Q

Seating arrangements are a common real-world puzzle — from planning a wedding dinner to arranging students in an exam hall.

+Worked Examplesi1 question
  1. Example 14Five children are sitting in a row. Shiva is sitting next to Priya but not Diya. Kavya is sitting next to Riya who is sitting on extreme lef…Preview
+Exercise 2.5i7 questions
  1. Q1Six students P, Q, R, S, T and U are sitting in two rows, three are in each row. T is not at the end of any row. S is second to the left of…Free
  2. Q2Group of 8 persons A, B, C, D, E, F, G and H are seated around a square table while facing towards each other, two persons are seated on eac…Free
  3. Q3Riya is known for her good photography skill and has won many prizes. On the occasion of family function five cousins approached her for cli…Free
  4. Q4In an exhibition seven different electronic companies are displaying their new Air Conditioner Model on seven different tables - LG, LLOYD,…Preview
  5. Q5Three Doctors Dr. Aggarwal, Dr. Chabbra and Dr. Roy are available in LIFE hospital of New Delhi. Dr. Aggarwal is available in hospital betwe…Preview
  6. Q6Five friends are standing in a line and facing towards the wall wearing Red, Grey, Yellow, Violet and Black Shoes. The persons wearing Yello…Preview
  7. Q7Six persons P, Q, R, S, T and U are sitting in a circle with their faces towards the centre. S is on the immediate left of T, P is on the le…Preview