SSS2 Math Quiz 7.3 – Bisector of an angle in a triangle

A car travels at a certain speed for 3 hours. Then, it travels at twice the speed for 2 hours. If the total distance covered is 240 km, find the speed of the car.

If the difference between two numbers is 7 and their sum is 47, find the numbers.

A father is three times as old as his son. In 12 years, the father will be twice as old as his son. Find their present ages.

A train travels a distance of 450 km at a certain speed. If the train had traveled 75 km/hr faster, it would have taken 1 hour less to cover the same distance. Find the original speed of the train.

The sum of the digits of a two-digit number is 8. If the digits are reversed, the new number is 18 less than the original number. Find the original number.

A bottle contains a mixture of water and juice in the ratio of 5:3. If 3 liters of juice are added to the bottle, the ratio becomes 5:4. Find the total quantity of the mixture in the bottle.

Two numbers differ by 6. If three times the smaller number is added to the larger number, the result is 33. Find the numbers.

A garden is 8 meters longer than it is wide. If the perimeter is 48 meters, find the dimensions of the garden.

A man buys a certain number of apples at 4 for $1 and the same number at 3 for $1.50. If he sells all the apples at 5 for $2, he makes a profit of $6. Find the number of apples he bought.

The ratio of the present ages of Peter and his father is 1:5. In 10 years, the ratio of their ages will be 1:3. Find their present ages.

The length of a rectangle is twice its width. If the area of the rectangle is 192 square meters, find its dimensions.

A number is divided into two parts in the ratio of 3:5. If the smaller part is 15, find the number.

The sum of three consecutive odd integers is 69. Find the integers.

A box contains a certain number of red and blue balls in the ratio of 4:3. If 6 blue balls are added to the box, the ratio becomes 4:5. Find the total number of balls in the box.

The perimeter of a square is 40 cm. Find its area.

A boat travels 15 km downstream in 2 hours and the same distance upstream in 5 hours. Find the speed of the stream.

The sum of two numbers is 35. If the larger number is 3 more than 4 times the smaller number, find the numbers.

A man invested $12,000 in two accounts, one offering 8% interest per annum and the other offering 10% interest per annum. If the total interest earned after one year is $1,040, find the amount invested in each account.

The length of a rectangle is 6 cm more than its width. If the area of the rectangle is 180 square centimeters, find its dimensions.

A triangle has one angle that is 40 degrees more than the smallest angle, and the third angle is three times the smallest angle. Find the measures of all three angles.