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Worksheet: Ratio Among Three Numbers

In this worksheet, we will practice simplifying and using 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.

  • A 5 1 0 3 1
  • B 1 1 3 0
  • C 3 1 7 3 1
  • D 2 4 3 1
  • E 1 0 2 0 3 1

Q2:

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

  • A 0 . 4 ∶ 0 . 3 ∶ 0 . 8
  • B 4 ∶ 8 ∶ 3
  • C 0 . 4 ∶ 0 . 8 ∶ 0 . 3
  • D 4 ∶ 3 ∶ 8

Q3:

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

  • A 1 0 ∶ 1 ∶ 1
  • B 2 0 ∶ 1 ∶ 2
  • C 1 0 ∶ 2 ∶ 1
  • D 2 0 ∶ 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.

  • A 1 8 ∶ 3 ∶ 1 8 5
  • B 3 6 ∶ 3 7 ∶ 6
  • C 1 8 ∶ 1 8 5 ∶ 3
  • D 3 6 ∶ 6 ∶ 3 7

Q5:

Daniel, Noah, and Ethan saved 162 LE, 144 LE, and 108 LE respectively. Find the ratio of Daniel’s savings to those of Noah to those of Ethan.

  • A
  • B
  • C
  • D

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.

  • Athe price of the oven =7 539 LE, the price of the fridge =7 535 LE
  • Bthe price of the oven =7 543 LE, the price of the fridge =7 547 LE
  • Cthe price of the oven =5 026 LE, the price of the fridge =2 154 LE
  • Dthe price of the oven =11 310 LE, the price of the fridge =26 390 LE

Q8:

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

  • AElizabeth =5 319 LE, Amelia =13 297 LE, Liam =26 594 LE
  • BElizabeth =10 047 LE, Amelia =25 117 LE, Liam =10 047 LE
  • CElizabeth =13 563 LE, Amelia =22 605 LE, Liam =9 042 LE
  • DElizabeth =8 220 LE, Amelia =20 550 LE, Liam =16 440 LE

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.

  • A 1 ∶ 1 ∶ 1
  • B 7 ∶ 8 ∶ 5
  • C 8 ∶ 7 ∶ 1 5
  • D 8 ∶ 7 ∶ 5
  • E 8 ∶ 2 1 ∶ 5

Q10:

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

  • A50, 25
  • B16, 25
  • C50, 125
  • D16, 10

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?

  • A First factory = 4 2 9 , second factory = 2 6 4 , third factory = 6 6 0
  • B First factory = 3 5 3 , second factory = 1 6 3 , third factory = 4 0 7
  • C First factory = 6 1 0 6 , second factory = 2 8 7 2 , third factory = 7 0 3 0
  • D First factory = 6 0 0 6 , second factory = 2 7 7 2 , third factory = 6 9 3 0

Q12:

A business makes 75 000 LE profit in its first year. Daniel worked there for the whole year. Michael joined later in the year, missing the first 5 months. Anthony 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?

  • ADaniel’s share =5 727 LE, Michael’s share =28 637 LE, Anthony’s share =51 546 LE
  • BDaniel’s share =42 955 LE, Michael’s share =15 341 LE, Anthony’s share =27 614 LE
  • CDaniel’s share =39 651 LE, Michael’s share =16 521 LE, Anthony’s share =29 738 LE
  • DDaniel’s share =46 860 LE, Michael’s share =27 335 LE, Anthony’s share =11 715 LE

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?

  • Athe first person: 466 375 LE, the second person: 352 625 LE, the third person: 91 000 LE
  • Bthe first person: 56 375 LE, the second person: 42 625 LE, the third person: 591 000 LE
  • Cthe first person: 378 681 LE, the second person: 286 319 LE, the third person: 665 000 LE
  • Dthe first person: 353 625 LE, the second person: 267 375 LE, the third person: 69 000 LE

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?

  • A 1 ∶ 4 ∶ 3
  • B 6 ∶ 4 ∶ 1
  • C 1 ∶ 2 ∶ 3
  • D 1 ∶ 4 ∶ 6

Q15:

Ethan has of the amount of money that Liam has. Daniel has of the amount of money that Liam has. What is the ratio of Ethan’s money Liam’s money Daniel’s money in its simplest form?

  • A
  • B
  • C
  • D

Q16:

The ratio between the heights of three buildings A, B, and C is . If the height of building A is 60 meters, find the heights of building B and building C.

  • Aheight of building B 40 m , height of building C 30 m
  • Bheight of building B 4 m , height of building C 3 m
  • Cheight of building B 24 m , height of building C 45 m
  • Dheight of building B 24 m , height of building C 18 m

Q17:

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

  • A 6 0 ∶ 6 6 ∶ 5 5
  • B 1 0 ∶ 1 1 ∶ 1 2
  • C 5 5 ∶ 6 0 ∶ 6 6
  • D 6 6 ∶ 6 0 ∶ 5 5

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?

  • A first person’s share =19 125 LE, second person’s share =16 875 LE, third person’s share =36 000 LE
  • B first person’s share =12 750 LE, second person’s share =11 250 LE, third person’s share =48 000 LE
  • C first person’s share =38 250 LE, second person’s share =33 750 LE, third person’s share =36 000 LE
  • D first person’s share =25 500 LE, second person’s share =22 500 LE, third person’s share =24 000 LE

Q19:

Ethan, Jacob and Liam started a business together. The first year’s profit was 148 000 LE. Ethan was given of this profit as payment for his management work. The rest of the profit was distributed between them in the ratio . How much did each of them receive in total?

  • AEthan = 39 467 LE, Jacob = 29 600 LE, Liam = 78 933 LE
  • BEthan = 54 267 LE, Jacob = 29 600 LE, Liam = 78 933 LE
  • CEthan = 35 520 LE, Jacob = 26 640 LE, Liam = 71 040 LE
  • DEthan = 50 320 LE, Jacob = 26 640 LE, Liam = 71 040 LE

Q20:

Some money is shared between Jennifer, Michael and Daniel in the ratio . Jennifer’s share exceeds Daniel’s share by 875 LE. How much money do each of them receive?

  • AJennifer = 451 LE, Michael = 145 LE, Daniel = 729 LE
  • BJennifer = 411 LE, Michael = 77 LE, Daniel = 386 LE
  • CJennifer = 14 100 LE, Michael = 2 725 LE, Daniel = 13 225 LE
  • DJennifer = 14 000 LE, Michael = 2 625 LE, Daniel = 13 125 LE

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.

  • A capital of the first =10 228 LE, capital of the second =51 140 LE, capital of the third =97 166 LE
  • B capital of the first =228 LE, capital of the second =1 140 LE, capital of the third =2 166 LE
  • C capital of the first =6 466 LE, capital of the second =46 466 LE, capital of the third =91 466 LE
  • D capital of the first =9 772 LE, capital of the second =48 860 LE, capital of the third =92 834 LE
  • E capital of the first =13 534 LE, capital of the second =53 534 LE, capital of the third =98 534 LE

Q22:

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

  • A6 : 11 : 14
  • B2 : 7 : 10
  • C2 : 3 : 4
  • D2 : 4.5 : 6
  • E8 : 27 : 36

Q23:

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

  • A 5 6 ∶ 2 1 ∶ 2 4
  • B 6 4 ∶ 2 4 ∶ 2 1
  • C 2 1 ∶ 5 6 ∶ 6 4
  • D 3 ∶ 8 ∶ 7

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?

  • A first person’s share =61 091 LE, second person’s share =34 909 LE, third person’s share =122 182 LE
  • B first person’s share =46 345 LE, second person’s share =26 483 LE, third person’s share =23 172 LE
  • C first person’s share =37 333 LE, second person’s share =21 333 LE, third person’s share =74 667 LE
  • D first person’s share =26 880 LE, second person’s share =15 360 LE, third person’s share =53 760 LE

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.

  • Afirst weight = 29 kg, third weight = 8 kg
  • Bfirst weight = 79 kg, third weight = 74 kg
  • Cfirst weight = 116 kg, third weight = 16 kg
  • Dfirst weight = 406 kg, third weight = 203 kg

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