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In this lesson, we will learn how to simplify and use the ratio between three numbers to solve problems.

Q1:

The side lengths of a triangle are in the ratio 1 5 ∶ 1 2 ∶ 1 3 . Given that the triangle’s perimeter is 11, find the length of the shortest side.

Q2:

Express the ratio 4 . 4 ∶ 3 . 3 ∶ 8 . 8 in its simplest form.

Q3:

Determine the ratio between the three numbers 𝑎 , 𝑏 , and 𝑐 given that 𝑎 ∶ 𝑏 = 1 0 ∶ 1 and 𝑏 ∶ 𝑐 = 2 ∶ 1 .

Q4:

Determine the ratio of the quantities 9 ∶ 1 1 2 ∶ 9 2 5 0 k g k g g in its simplest form.

Q5:

Adam, Fares, and Shady saved 162 LE, 144 LE, and 108 LE respectively. Find the ratio of Adam’s savings to those of Fares to those of Shady.

Q6:

The ratios 12 : 4 : 8 and 𝑥 5 𝑦 : : are equivalent.

Find 𝑥 .

Find 𝑦 .

Q7:

The ratio of the prices of a television, an oven and a fridge is 2 ∶ 3 ∶ 7 respectively. Given that the television costs 7 540 LE, calculate the prices of the oven and the fridge.

Q8:

Three people start a company and decide to share the profits in the same ratio as their investments in the company. Mona invested 2 5 of the amount that Dina invested. Amir invested twice the amount that Mona invested. At the end of the first year the total profit is 45 210 LE. Calculate each person’s share of this profit.

Q9:

A man has three sticks. The length of the first stick is 2.4 m, the length of the second is 2.1 m, and the length of the third is 1.5 m. Find the ratio between their lengths, respectively, in its simplest form.

Q10:

Complete the following putting the ratio in its simplest form: 2 5 ∶ 1 4 ∶ 5 8 = ∶ ∶ 2 5 .

Q11:

Three factories manufacture identical products in the ratio 1 3 ∶ 6 ∶ 1 5 . The third factory makes 924 more products than the first factory in one month. How many products does each factory make that month?

Q12:

A business makes 75 000 LE profit in its first year. Adam worked there for the whole year. Fady joined later in the year, missing the first 5 months. Shady also joined later in the year, missing the first 9 months. They agreed to share the profits in the ratio of the number of months each was working for the business. What share of the profits did each person get?

Q13:

Three people started a company and decided to share the profits and losses in the same ratio as their investments in the company. The first invested 410 000 LE, the second invested 310 000 LE, and the third invested 1 9 of the sum of the investments of the other two. During the first year the company made a loss of 110 000 LE, which was proportionally deducted from each person’s investment. How much money did each person have left in their investment after the deductions?

Q14:

In a basket of fruit, the ratio of the weight of guavas to the weight of bananas is 1 ∶ 4 . The ratio of the weight of bananas to the weight of apples is 2 ∶ 3 . What is the ratio of the weights of guavas, bananas and apples in its simplest form?

Q15:

Sherif has 2 2 1 7 of the amount of money that Amir has. Adam has 7 8 of the amount of money that Amir has. What is the ratio of Sherif’s money ∶ Amir’s money ∶ Adam’s money in its simplest form?

Q16:

The ratio between the heights of three buildings A, B, and C is 1 0 ∶ 4 ∶ 3 . If the height of building A is 60 metres, find the heights of building B and building C.

Q17:

If 1 0 𝑥 = 1 1 𝑦 = 1 2 𝑧 , find 𝑥 ∶ 𝑦 ∶ 𝑧 .

Q18:

Three people invested money in a business and decided to share the profits in the same ratio as their investments. The first invested 51 000 LE, the second invested 45 000 LE, and the third invested half the sum of the other two’s investments. After one year the profit of 72 000 LE was shared out. How much profit did each person receive?

Q19:

Sherif, Bassem and Amir started a business together. The first year’s profit was 148 000 LE. Sherif was given 1 1 0 of this profit as payment for his management work. The rest of the profit was distributed between them in the ratio 4 ∶ 3 ∶ 8 . How much did each of them receive in total?

Q20:

Some money is shared between Engy, Fady and Adam in the ratio 1 6 ∶ 3 ∶ 1 5 . Engy’s share exceeds Adam’s share by 875 LE. How much money do each of them receive?

Q21:

Three people opened a new restaurant; the first invested 10 000 LE, the second invested 50 000 LE, and the third invested 95 000 LE. At the end of the first year, the restaurant lost 3 534 LE which was deducted from the capital. Calculate the capital of each person at the beginning of the second year.

Q22:

Which of the following ratios is equivalent to 4 : 9 : 12?

Q23:

If 𝑎 = 3 8 𝑏 and 𝑏 = 8 7 𝑐 , then express the ratio 𝑎 ∶ 𝑏 ∶ 𝑐 in its simplest numeric form.

Q24:

Three people invested money in a project and decided to share the profits in the same ratio as their investments. The first invested 14 000 LE, the second invested 8 000 LE, and the third invested twice the amount of the first. At the end of the first year a profit of 96 000 LE was shared between the investors. How much did each of them receive?

Q25:

The weights of three containers are in the ratio 1 4 ∶ 2 ∶ 7 . The weight of the second container is 58 kg. Calculate the weights of the first and third containers.

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