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Questions and Answers
If the price of a book is increased by 20% and then decreased by 10%, what is the net percentage change in the price?
If the price of a book is increased by 20% and then decreased by 10%, what is the net percentage change in the price?
- 8% decrease (correct)
- 8% increase
A student scored 65% marks in one subject and 75% marks in another subject. What is the overall percentage of marks obtained by the student if both subjects carry equal weightage?
A student scored 65% marks in one subject and 75% marks in another subject. What is the overall percentage of marks obtained by the student if both subjects carry equal weightage?
70%
If the final salary is $10,500 after a 10% increase in the first year and a 5% decrease in the second year, what was the initial salary?
If the final salary is $10,500 after a 10% increase in the first year and a 5% decrease in the second year, what was the initial salary?
$10,000
If the price of a commodity increases by 25%, by what percent must its consumption be reduced to not increase the expenditure?
If the price of a commodity increases by 25%, by what percent must its consumption be reduced to not increase the expenditure?
If 60% of 240 students passed an examination, how many students failed?
If 60% of 240 students passed an examination, how many students failed?
If a shopkeeper sold a T-shirt at a 25% profit with a cost price of $40, what was the selling price?
If a shopkeeper sold a T-shirt at a 25% profit with a cost price of $40, what was the selling price?
If an amount doubles in 5 years at simple interest, what is the rate of interest per annum?
If an amount doubles in 5 years at simple interest, what is the rate of interest per annum?
Find the smallest positive integer n such that $n^2 + 25$ is divisible by 5.
Find the smallest positive integer n such that $n^2 + 25$ is divisible by 5.
If a + b + c = 6, ab + bc + ca = 11, and abc = 6, find the value of $a^3 + b^3 + c^3 - 3abc$.
If a + b + c = 6, ab + bc + ca = 11, and abc = 6, find the value of $a^3 + b^3 + c^3 - 3abc$.
In triangle ABC where angle A = 90°, AB = 6, and BC = 8, what is the length of AC?
In triangle ABC where angle A = 90°, AB = 6, and BC = 8, what is the length of AC?
In how many ways can 5 boys and 5 girls be seated in a row such that no two boys are together?
In how many ways can 5 boys and 5 girls be seated in a row such that no two boys are together?
From a box with 5 red balls, 4 blue balls, and 3 green balls, if 2 balls are drawn randomly, what is the probability that both are blue?
From a box with 5 red balls, 4 blue balls, and 3 green balls, if 2 balls are drawn randomly, what is the probability that both are blue?
If a cone is inscribed in a hemisphere with a hemisphere radius of 6 cm, what is the volume of the cone?
If a cone is inscribed in a hemisphere with a hemisphere radius of 6 cm, what is the volume of the cone?
A can do a piece of work in 6 days, B can do it in 8 days. They work together for 3 days and then A leaves. In how many more days will B finish the remaining work?
A can do a piece of work in 6 days, B can do it in 8 days. They work together for 3 days and then A leaves. In how many more days will B finish the remaining work?
A shopkeeper marks his goods 50% above cost price, then allows a 20% discount and sells for $160. Find the cost price of the article.
A shopkeeper marks his goods 50% above cost price, then allows a 20% discount and sells for $160. Find the cost price of the article.
If a city's population increased by 20% in the first year and decreased by 10% in the second year, what is the net percentage increase or decrease in population?
If a city's population increased by 20% in the first year and decreased by 10% in the second year, what is the net percentage increase or decrease in population?
A cuboid with dimensions 6 cm x 8 cm x 10 cm has a cube cut from it. What is the surface area of the remaining part?
A cuboid with dimensions 6 cm x 8 cm x 10 cm has a cube cut from it. What is the surface area of the remaining part?
A solid sphere of radius 6 cm is melted and recast into small spheres of radius 3 cm. How many small spheres can be formed?
A solid sphere of radius 6 cm is melted and recast into small spheres of radius 3 cm. How many small spheres can be formed?
A cylindrical pipe with inner radius 4 cm and thickness 1 cm, and length 50 cm. What is the volume of the material used in making the pipe?
A cylindrical pipe with inner radius 4 cm and thickness 1 cm, and length 50 cm. What is the volume of the material used in making the pipe?
A conical vessel with height 16 cm and base diameter 14 cm is full of water. Find the volume of the water in the vessel.
A conical vessel with height 16 cm and base diameter 14 cm is full of water. Find the volume of the water in the vessel.
A frustum of a cone with diameters 12 cm and 20 cm and height 16 cm. Find its volume.
A frustum of a cone with diameters 12 cm and 20 cm and height 16 cm. Find its volume.
A hemisphere is cut out from a solid wooden cube with side 21 cm. What is the surface area of the remaining solid?
A hemisphere is cut out from a solid wooden cube with side 21 cm. What is the surface area of the remaining solid?
A solid wooden cube of side 10 cm is cut into eight cubes of equal volume. What is the total surface area of all the small cubes?
A solid wooden cube of side 10 cm is cut into eight cubes of equal volume. What is the total surface area of all the small cubes?
A regular square pyramid with base side length 6 cm and slant height 8 cm. Find its total surface area.
A regular square pyramid with base side length 6 cm and slant height 8 cm. Find its total surface area.
A cylindrical glass filled with water to the brim has diameter 14 cm and height 10 cm. If the water is poured into a rectangular vessel with base area 140 sq.cm, find the height of the water level in the vessel.
A cylindrical glass filled with water to the brim has diameter 14 cm and height 10 cm. If the water is poured into a rectangular vessel with base area 140 sq.cm, find the height of the water level in the vessel.
An irregular block of wood 10 cm long, 6 cm wide, 4 cm high is cut into small cubes of side 2 cm. What is the total number of cubes?
An irregular block of wood 10 cm long, 6 cm wide, 4 cm high is cut into small cubes of side 2 cm. What is the total number of cubes?
A sum of $5000 is lent at a certain rate of interest for 2 years, compounded annually. If the amount after 2 years is $5500, find the rate of interest.
A sum of $5000 is lent at a certain rate of interest for 2 years, compounded annually. If the amount after 2 years is $5500, find the rate of interest.
Find the compound interest on $10,000 at 10% per annum for 2 years, compounded quarterly.
Find the compound interest on $10,000 at 10% per annum for 2 years, compounded quarterly.
John invested a sum of money at 5% interest compounded annually. After 4 years, he received $3000. Find the sum he invested.
John invested a sum of money at 5% interest compounded annually. After 4 years, he received $3000. Find the sum he invested.
A sum of money amounts to $9680 in 2 years and $10648 in 3 years when compounded annually. Find the sum and the rate of interest.
A sum of money amounts to $9680 in 2 years and $10648 in 3 years when compounded annually. Find the sum and the rate of interest.
The simple interest on a certain sum for 3 years at 12% per annum is $5400. Find the sum.
The simple interest on a certain sum for 3 years at 12% per annum is $5400. Find the sum.
Find the compound interest on $5000 at 10% per annum for 2 years, compounded half-yearly.
Find the compound interest on $5000 at 10% per annum for 2 years, compounded half-yearly.
A sum of money becomes 3 times itself in 5 years at simple interest. What is the annual rate of interest?
A sum of money becomes 3 times itself in 5 years at simple interest. What is the annual rate of interest?
Find the compound interest on $4000 at 8% per annum for 2 years, compounded annually.
Find the compound interest on $4000 at 8% per annum for 2 years, compounded annually.
A sum of money becomes 5/4 times itself in 2 years at simple interest. What is the rate of interest?
A sum of money becomes 5/4 times itself in 2 years at simple interest. What is the rate of interest?
At what rate of interest per annum will a sum of money double itself in 5 years, compounded annually?
At what rate of interest per annum will a sum of money double itself in 5 years, compounded annually?
In triangle ABC where angle A = 60°, angle B = 75°, and AC = 6 cm, find the length of side BC.
In triangle ABC where angle A = 60°, angle B = 75°, and AC = 6 cm, find the length of side BC.
In a rectangle, if the length is 6 cm more than the breadth and the diagonal is 10 cm, find the area.
In a rectangle, if the length is 6 cm more than the breadth and the diagonal is 10 cm, find the area.
In a cyclic quadrilateral ABCD where AB = 6 cm, BC = 8 cm, CD = 4 cm, and angle ADC = 90°, find the length of AD.
In a cyclic quadrilateral ABCD where AB = 6 cm, BC = 8 cm, CD = 4 cm, and angle ADC = 90°, find the length of AD.
Given the radius of the incircle of a triangle is 4 cm and the radius of the circumcircle is 5 cm, find the area of the triangle.
Given the radius of the incircle of a triangle is 4 cm and the radius of the circumcircle is 5 cm, find the area of the triangle.
In a regular hexagon, find the ratio of the area of the inscribed circle to the area of the circumscribed circle.
In a regular hexagon, find the ratio of the area of the inscribed circle to the area of the circumscribed circle.
A triangle has sides of lengths 13 cm, 14 cm, and 15 cm. Find the length of the altitude drawn to the side of length 14 cm.
A triangle has sides of lengths 13 cm, 14 cm, and 15 cm. Find the length of the altitude drawn to the side of length 14 cm.
Two tangents to a circle from an external point are of lengths 8 cm and 12 cm. If the distance between the centers of the circle and the point is 10 cm, find the radius of the circle.
Two tangents to a circle from an external point are of lengths 8 cm and 12 cm. If the distance between the centers of the circle and the point is 10 cm, find the radius of the circle.
A parallelogram has adjacent sides of lengths 10 cm and 12 cm. If the distance between the longer sides is 8 cm, find the area.
A parallelogram has adjacent sides of lengths 10 cm and 12 cm. If the distance between the longer sides is 8 cm, find the area.
In a trapezium ABCD where AB || DC, AB = 8 cm, DC = 6 cm, and the height is 5 cm, find the length of side BC.
In a trapezium ABCD where AB || DC, AB = 8 cm, DC = 6 cm, and the height is 5 cm, find the length of side BC.
A square and a circle have the same perimeter. Find the ratio of the area of the square to the area of the circle.
A square and a circle have the same perimeter. Find the ratio of the area of the square to the area of the circle.
Study Notes
Here are the study notes for the provided text:
- Percentages*
- If the price of a book is increased by 20% and then decreased by 10%, the net percentage change in the price is an 8% increase.
- A student scored 65% marks in one subject and 75% marks in another subject, and the overall percentage of marks obtained is the average of the two subjects.
- If a salary is increased by 10% in the first year and decreased by 5% in the second year, the final salary can be found by applying the percentage changes successively.
- If the price of a commodity increases by 25%, the consumption must be reduced by 20% to not increase the expenditure.
- In an election, if 60% of the students passed, the number of students that failed can be found by subtracting the number of students that passed from the total number of students.
- Permutations and Combinations*
- A committee of 4 members can be chosen from 10 men and 5 women if the committee must consist of at least 2 men and 1 woman.
- Different words can be formed using the letters of the word "UNIQUE".
- A student can select 4 books if at least 2 books must be mathematics books.
- Different arrangements can be made from the letters of the word "COMPUTER" if the vowels must occupy the odd positions.
- A president, vice president, and treasurer can be selected from a group of 8 people if one person cannot hold more than one position.
- Different passwords can be formed using the English alphabet and digits 0-9 if repetition of characters is allowed.
- Clocks*
- The hands of a clock are together at 5:27:16 2/11 minutes past 5.
- The hands of a clock form a right angle 44 times in a day.
- The acute angle between the hour and minute hands of a clock at 4:20 is 120°.
- The hands of a clock overlap 22 times in a day.
- The minute hand and hour hand of a clock are perpendicular to each other at 7:21:49 1/11 minutes past 7.
- Calendars*
- 25 days ago, if today is Tuesday, the day of the week was Thursday.
- If 8th March 2024 is a Friday, 8th March 2044 is a Monday.
- The 13th of the month occurs 2 times in a non-leap year.
- If January 1, 2025, falls on a Tuesday, October 1, 2025, is a Wednesday.
- 333 days from today, if today is Monday, the day of the week is Wednesday.
- Time and Work*
- A, B, and C together can complete a piece of work in 4 days.
- A, B, and C together can complete a piece of work in 6 days.
- A and B together can complete a piece of work in 7.5 days.
- B and C together can complete a piece of work in 15 days.
- B can complete a piece of work in 12 days.
- Distance and Speed*
- The average speed of a car for the whole journey is 48 km/h.
- A train covers a distance of 600 km in 5 hours.
- A cyclist travels from town A to town B at a speed of 15 km/h.
- A car travels from city X to city Y at an average speed of 50 km/h.
- A boat travels upstream for 3 hours and covers a distance of 30 km.
- Mixed Questions*
- The smallest positive integer n such that n^2 + 25 is divisible by 5 is 5.
- a + b + c = 6, ab + bc + ca = 11, and abc = 6, then a^3 + b^3 + c^3 - 3abc = 72.
- In triangle ABC, angle A = 90°, AB = 6, and BC = 8, then the length of AC is 10.
- 5 boys and 5 girls can be seated in a row such that no two boys are together in 2400 ways.
- The probability that both balls are blue is 2/65.
- The volume of the cone is 144Ï€ / 5 cubic cm.
- Surface Area and Volumes*
- The surface area of the remaining part is 424 sq.cm.
- 64 small spheres can be formed from a solid sphere of radius 6 cm.
- The volume of the material used in making the pipe is 692Î cm^3.
- The volume of water in the vessel is 1232π cm³.
- The volume of the frustum of the cone is 400Ï€/3 cm^3.
- The surface area of the remaining solid is 441Ï€ sq.cm.
- Simple and Compound Interest*
- The rate of interest is 10% per annum.
- The compound interest is $2104.16.
- The sum invested is $2500.
- The sum and the rate of interest are $10,000 at 4% per annum.
- The simple interest is $5400.
- Geometry*
- The length of side BC is 2 root7 cm.
- The area of the rectangle is 24 sq.cm.
- The length of AD is 4 cm.
- The area of the triangle is 24 sq.cm.
- The ratio of the area of the inscribed circle to the area of the circumscribed circle is Root3 /2 : root3 /3.
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Description
Test your skills in percentages with these challenging multiple-choice questions. Calculate percentage changes, increases, and decreases in prices, marks, and salaries.
