Examples for secondary school students - page 2 of 232

Number of problems found: 4621

Alcohol mixture 3
A mixture contains alcohol and water in the ratio 4:3. If 7 litres of water are added, the ratio of alcohol to water becomes 3:4. Find the quantity of alcohol in the mixture.
Equation of the line
Find the equation of the line through (1, 2) with slope 3.
The sum 53
The sum of three numbers in a geometric progression is 35 and their product is 1,000. Find the numbers.
A train 7
A train overtakes two persons walking in the same direction as the train at speeds of 2 km/h and 4 km/h. The train passes each of them completely in 9 and 10 seconds respectively. Find the length of the train.
A person 3
A person distributes his pens among four friends A, B, C, and D in the ratio 1/3 : 1/4 : 1/5 : 1/6. What is the minimum number of pens the person should have?
A pie 16
A pie is divided among 100 guests. Guest 1 gets 1%, guest 2 gets 2% of what is left, and so on. Who gets the largest piece of pie?
The centroid
The centroid of a triangle ABC is at the point (3, 3, 3). If the coordinates of A and B are (3, −5, 7) and (−1, 7, −6) respectively, find the coordinates of point C.
Two types of ore
A total of 42 tonnes of two types of ore is to be fed into a smelter. The first type contains 6% copper and the other contains 2.5% copper. Find the necessary amounts of each ore to produce 2 tonnes of copper.
The Earth and Moon
The diameter of the Moon is approximately 1/4 of the diameter of the Earth. What fraction of the Earth's volume is the Moon's volume?
Parallel lines - dist
Find the distance between the parallel lines 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0.
A person 2
A person has 2 parents, 4 grandparents, 8 great-grandparents, and so on. Find the total number of ancestors during the ten generations preceding his own.
The sum 52
The sum of the digits of a two-digit number is 10. When the digits are interchanged, the resulting number is 54 less than the original. What is the original number?
Tower + pole
On horizontal ground, there is a vertical tower with a flagpole on its top. From a point 9 m from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60° and 30° respectively. Find the height of the flagpole.
The ratio 21
The ratio of the number of sides of two regular polygons is 1:2 and the ratio of the sum of their interior angles is 2:3. Find the number of sides of each polygon.
The ages 3
The ages of A and B are in the ratio 5:4. Three years from now, the ratio of their ages will be 11:9. What is B's present age?
A rectangle 15
A rectangle is 5 cm longer than its width. Its area is 6 cm². What are the dimensions of the rectangle?
A man 24
A man distributed €25,300 among his 3 sons A, B, and C such that the amounts of their portions, with 10% simple interest over 2 years, 3 years, and 4 years respectively, will be equal. What is A's share?
The rhombus (a,d)
Find the area of a rhombus, one side of which measures 20 cm and one diagonal of which is 24 cm.
Two masons
Mason A can build a wall in 30 days, while Mason B can build it in 40 days. If they build it together and receive a payment of $7,000, what is B's share?
A tree 3
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground at an angle of 30°. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the original height of the tree.

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