Week 7 Y6 Math Trial Test

A solution is 40 percent alcohol by volume.

How many litres of pure alcohol must be added to one litre of the solution to create a mixture that is 60 percent alcohol by volume?

It took a bus 7 hours to travel from Sunnydale to Greendale, a distance of 210 kilometres.

The bus covered the first 30 percent of the trip in 2 hours, and the rest of the trip in 5 hours.

The average speed of the bus during the first 2 hours of the trip was how many times the average speed of the bus during the last 5 hours of the trip?

A rabbit can run three times farther in 36 minutes than a turtle can run in 30 minutes.

If the rabbit runs at an average speed of 40 metres per hour, at what speed does the turtle run?

A tank full of water started leaking at a constant rate.

If it took 5 hours for a sixth of the water in the tank to leak, how many hours will it take for a quarter of the water in the tank to leak?

Mixture X is composed of cement and sand mixed in a ratio of 4 to 5, respectively.

Mixture Y is composed of cement and sand mixed in a ratio of 7 to 5, respectively.

If equal amounts of mixture X and mixture Y are mixed to create mixture Z, what is the ratio of cement to sand in mixture Z?

A fruit vendor purchased cantaloupes at a wholesale price of $10 per dozen.

The fruit vendor then sells the cantaloupes at a rate of $120 per hundred cantaloupes.

How much percent will the fruit vendor’s profit be if she sells all the cantaloupes? (Profit = Revenue – Expenses)

A bus, travelling at a constant speed, leaves Sunset Valley and heads towards Greendale, passing through the towns of Charleston and Raspberry, in that order, along the way.

It took the bus 7 hours to travel from Sunset Valley to Charleston, and another 5 hours to travel from Charleston to Raspberry.

If the distance from Sunset Valley to Charleston is 60 kilometres farther than the distance from Charleston to Raspberry, what is the distance from Sunset Valley to Raspberry?

A jeweller purchased 1 800 bracelets at a wholesale price of $12 each.

The jeweller sold 800 of the bracelets for $16 each and the rest of the bracelets for $10 each.

How much was the jeweller’s profit or loss from the sale of the bracelets?

Allan sold a dog house, with a regular price of $96, at a discount of 25 percent.

At this discounted price, Allan makes a profit of 20 percent on the cost of making the dog house.

How much did it cost Allan to make the dog house?

Box A contains black and white marbles only in the ratio of 5 to 3, respectively.

Box B contains black and white marbles only in the ratio of 5 to 11, respectively.

If all the marbles in box A and box B are combined, what will be the ratio of the number of black marbles to the number of white marbles?

Bernie, working alone at a constant rate, can complete the task in 4 hours.

Hank, working alone at a constant rate, can complete the same task in 8 hours.

If the two of them work together at their respective constant rates, how long will it take the two of them to complete the task?

Andrea works as a waitress at the local diner.

She is paid $10 per hour for the first 8 hours she works and 1.5 times that amount for each additional hour she works.

Yesterday, Andrea worked from 9:30 AM to 7:30 PM.

How much did Andrea get paid yesterday?

It takes machines A, B, and C, working together at their respective constant rates, hours to make 1 600 widgets.

If only machines A and B work together at their respective constant rates, it will take the two machines 4 hours to make 1 600 widgets.

How much time will it take machine C only to make 40 widgets?

The sum of the degree measures of angles ABC and XYZ is equal to 90°.

If the degree measure of angle ABC is three times the degree measure of XYZ, what is the degree measure of angle ABC?

There are 40 male cows and 50 female cows on Aunt Mary’s dairy farm.

Of all the cows on the dairy farm, 30 are not brown.

If half of the brown cows on the farm are female, how many male cows are not brown?

Last year, Belinda’s annual income was $240 000.

This year, her annual income was $288 000.

By how much percent did her annual income increase from last year to this year?

A box contains 8 kilograms of cement mixture that is 5 percent cement by mass.

If 1 kilogram of pure sand is removed from the box, the resulting mixture is what percent cement by mass?

Peter’s hourly rate was increased by 10 percent.

Before the increase in his hourly rate, Peter earns $2 260 each week.

If the total number of hours Peter worked each week were decreased by 10 percent after the increase in his hourly rate, by how much will his total weekly earnings change because of the increase in his hourly rate?

Ruben rode his bike from his house to the mall, a distance of 25 kilometres.

On his way to the mall, he biked at an average speed of 4 kilometres per hour.

On his way back to his house, he biked along the same route at an average speed of 2 kilometres per hour.

What was his average speed for the entire trip?

Six weeks ago, Anthony planted a tree in his backyard that was only 198 centimetres tall.

The tree was already 222 centimetres tall today.

If the tree continues to grow at the same average weekly rate, in how many weeks from today will the tree be 240 centimetres tall?

An online website is selling a total of 675 tickets for a concert.

Initially, the website sold 16 percent of the tickets during the first 88 minutes.

If the initial rate at which the tickets were sold was doubled, in how many minutes will the website sell the rest of the tickets?

Carol put a rectangular box on a display cabinet.

The area of the front face of the box is half the area of the top face of the box, and the area of the top face of the box is 1 1/2 times the area of the side face of the box.

If the box has a volume of 3 cubic metres, what is the area of the side face of the box?

Of all the balls coloured red in the box, 30 percent have a matte finish.

If 18 percent of the total number of balls in the box are red balls with a matte finish, what percent of the total number of balls in the box is coloured red?