Solving problem sums involving multiple ratios for different items but has 1 common item

An example from our high quality Primary Mathematics Tuition

How To Identify Such Problems

Such problems will typically have all of the following:

1. Involves 3 (or more) persons/objects

2. Two sets of ratios between 2 of the persons/objects are provided.

3. There is a common item between the two ratios

4. Quantity information information of 1 of the persons/objects, or between two persons/objects

5. Need to find the quantity of a specific person/object

*Don’t worry if you don’t fully understand above at this point. Use the following example to help you with your understanding. Come back here again after you have gone through the rest of the tip.

An Example Problem

Alicia and Betty had a number of sweets in the ratio of 2:5. Alicia and Chloe had a number of sweets in the ratio of 3:1. If they had a total of 184 sweets, how many sweets did Chloe have? 

Breaking Down the Example Problem

• The persons/objects involved: 

  • Alicia (A)

  • Betty (B)

  • Chloe (C)

• The ratios information provided: 

  • A : B = 2 : 5

  • A : C = 3 : 1 

• Common person in the ratio information: Alicia (A)

• Quantity information: A + B + C = 184

• Problem to solve: C = ? 

General Technique To Use

You can follow the following steps to solve such problems:

1. Clearly write down the the two ratios

2. Identify the common person/item

3. Adjust the two ratios so that the number for the common item is the same

4. Create a single ratio for all three items

5. Use the quantity information to calculate the value to each unit

6. Solve the question

*Don’t worry if you don’t fully understand the above. Use the following example to help you with your understanding. Come back here again after you have gone through the step-by-step solution of the example problem.

Solving the Example Problem (Step-By-Step Guide)

More Similar Problems

1. Alicia and Betty had a number of sweets in the ratio of 2:5. Alicia and Chloe had a number of sweets in the ratio of 3:1. If Betty had 90 more sweets than Alicia, how many sweets did Chloe have? (Hint: This is a slight variation from the example problem)

2. Alicia and Betty had a number of sweets in the ratio of 2:5. Alicia and Chloe had a number of sweets in the ratio of 3:1. If Alicia and Betty had a total of 210 sweets, how many sweets did Chloe have? (Hint: This is a slight variation from the example problem)

3. Derick, Eileen and Fabian share some cookies. The ratio of Eileen’s cookies to Derick’s cookie’s is 3:5. The ratio of Derick’s cookie’s to Fabian’s cookies is 4:1. Given that Derick had 160 more cookies than Eileen, what is the total number of cookies?