FREE RCMP Problem Solving Questions and Answers
Discount appliance store employees are entitled to an extra 20% off the lowest price on any item. How much will an employee spend for a $450 dishwasher if he buys it during a 15% off sale?
Explanation:
The original price of the dishwasher is $450. During a 15% off sale, the price of the dishwasher will be reduced by:
15% of $450 = 0.15 x $450 = $67.50
So the sale price of the dishwasher will be:
$450 – $67.50 = $382.50
As an employee, the person receives an additional 20% off the lowest price, which is $382.50. We can calculate the additional discount as:
20% of $382.50 = 0.20 x $382.50 = $76.50
So the final price that the employee will pay for the dishwasher is:
$382.50 – $76.50 = $306.00
Therefore, the employee will pay $306.00 for the dishwasher.
How long will it take for both Tracy and Kevin to paint a house if Tracy can do it in four hours and Kevin can finish it in six?
Explanation:
This is an inverse ratio problem
1/x = 1/a + 1/b where a is the time Sally can paint a house, b is the time John can paint a house, x is the time Sally and John can together paint a house
So,
1/x = 1/4 + 1/6 … We use the least common multiple in the denominator that is 24:
1/x = 6/24 + 4/24
1/x = 10/24
x = 24/10
x = 2.4 hours
In other words; 2 hours + 0.4 hours = 2 hours + 0.4•60 minutes
= 2 hours 24 minutes
Every week, Mark pays each of his "n" employees a sum equal to "s." In what number of days can he hire these 'n' people if he has 'x' amount of money?
Explanation:
We are given that each of the n employees earns s amount of salary weekly. This means that one employee earns s salary weekly. So; Mark has ‘ns’ amount of money to employ n employees for a week.
We are asked to find the number of days n employees can be employed with x amount of money. We can do simple direct proportion:
If Mark can employ n employees for 7 days with ‘ns’ amount of money,
Mark can employ n employees for y days with x amount of money … y is the number of days we need to find.
We can do cross multiplication:
y = (x * 7)/(ns)
y = 7x/ns
What portion of the page can Mary type in five minutes if she can type a page in p minutes?
Explanation:
This is a simple direct proportion problem:
If Lynn can type 1 page in p minutes, then she can type x pages in 5 minutes
We do cross multiplication: x * p = 5 * 1
Then,
x = 5/p
If Mr. Smith distributes half of his income to his family, $250 to his landowner, and leaves exactly 3/7 of his pay behind, how much does he receive?
Explanation:
We check the fractions taking place in the question. We see that there is a “half” (that is 1/2) and 3/7. So, we multiply the denominators of these fractions to decide how to name the total money. We say that Mr. Smith has 14x at the beginning; he gives half of this, meaning 7x, to his family. $250 to his landlord.
He has 3/7 of his money left. 3/7 of 14x is equal to:
14x * (3/7) = 6x
So,
Spent money is: 7x + 250
Unspent money is: 6×51
Total money is: 14x
Write an equation: total money = spent money + unspent money
14x = 7x + 250 + 6x
14x – 7x – 6x = 250
x = 250
We are asked to find the total money that is 14x:
14x = 14 * 250 = $3500
A weaving plant manager calculates that 10 machines operating at full capacity for eight hours will yield 1450 meters of cloth. Owing to various technical issues, 6 machines operate at 90% efficiency while 4 operate at 95% efficiency. In eight hours, how many meters of cloth can be produced by these machines?
Explanation:
At 100% efficiency 1 machine produces 1450/10 = 145 m of cloth
At 95% efficiency, 4 machines produce 4 * 145 * 95/100 = 551 m of cloth
At 90% efficiency, 6 machines produce 6 * 145 * 90/100 = 783 m of cloth
Total cloth produced by all 10 machines = 551 + 783 = 1334 m
Since the information provided and the question are based on 8 hours, we did not need to use time to reach the answer.
There are 28 blue pencils and 7 black pencils in a box. What is the ratio of the blue and black pens?
Explanation:
The ratio between black and blue pens is 7 to 28 or 7:28. Bring to the lowest terms by dividing both sides by 7 gives 1:4.
A car is being sold for $12,590, which is 20% less than it originally cost. What was the initial cost?
Explanation:
Original price = x,
80/100 = 12590/X,
80X = 1259000,
X = 15,737.50.
There were 1270 registered voters at polling station A, and 945 of them cast ballots in the local election. Out of 1050 registered voters, 860 people voted at polling station B, while 1210 people voted at polling station C out of 1440 registered voters. How many people visited each of the three polling places overall?
Explanation:
The turnout at polling station A is 945 out of 1270 registered voters. So, the percentage turnout at station A is:
(945/1270) × 100% = 74.41%
The turnout at polling station B is 860 out of 1050 registered voters. So, the percentage turnout at station B is:
(860/1050) × 100% = 81.90%
The turnout at polling station C is 1210 out of 1440 registered voters. So, the percentage turnout at station C is:
(1210/1440) × 100% = 84.03%
To find the total turnout from all three polling stations, we need to add up the total number of voters and the total number of registered voters from all three stations:
Total number of voters = 945 + 860 + 1210 = 3015
Total number of registered voters = 1270 + 1050 + 1440 = 3760
The overall percentage turnout is:
(3015/3760) × 100% = 80.12%
Therefore, the total turnout from all three polling stations is 80.12% — rounding to 80%.
For $165, a distributor bought 550 kg of potatoes. He gave these away to 15 businesses for $6.4 per 20 kilos, 12 shops for $3.4 per 10 kilograms, and the other shops for $1.8 per 5 kilograms. What will he make if his distribution costs total $10?
Explanation:
The distribution is done at three different rates and in three different amounts:
$6.4 per 20 kilograms to 15 shops … 20•15 = 300 kilograms distributed
$3.4 per 10 kilograms to 12 shops … 10•12 = 120 kilograms distributed
550 – (300 + 120) = 550 – 420 = 130 kilograms left. This 50
amount is distributed in 5-kilogram portions. So, this means that there are 130/5 = 26 shops.
$1.8 per 130 kilograms.
We need to find the amount he earned overall in these distributions.
$6.4 per 20 kilograms : 6.4•15 = $96 for 300 kilograms
$3.4 per 10 kilograms : 3.4 *12 = $40.8 for 120 kilograms
$1.8 per 5 kilograms : 1.8 * 26 = $46.8 for 130 kilograms
So, he earned 96 + 40.8 + 46.8 = $ 183.6
The total distribution cost is given as $10
The profit is found by: Money earned – money spent … It is important to remember that he bought 550 kilograms of potatoes for $165 at the beginning:
Profit = 183.6 – 10 – 165 = $8.6
Canvas waterproofing costs fifty cents per square yard. How much will it cost to waterproof a 15' by 24' canvas truck cover?
Explanation:
First calculate total square feet, which is 15 * 24 = 360 ft2. Next, convert this value to square yards, (1 yards2 = 9 ft2) which is 360/9 = 40 yards2. At $0.50 per square yard, the total cost is 40 * 0.50 = $20.