Compound ratio

Ratio is comparing of two quantities that are having same units. For example, the ratio of Indian citizens to American citizens is 45:50. The symbol : is pronounced as isto.

Symbolically, the ratio can be written as a:b, where a is antecedent and b is consequent.

What is compound ratio?

Compound ratio is the method of comparing two or more ratios.

In other words, Product of two antecedents isto product of two consequents.

For example, a:b and p:q can be written as ap:bq

Formula for compound ratio

Let us take 2 ratios, j:k and l:m

This can be written as jk and lm

When we multiply both the terms we get

                           jklm

By cross multiplying them we get

• jm × lk

Which can written in the form of

• jm:lk

Simply the formula of compound interest is a and b : c and d can be written as ac:bd

For example,

A work can be completed in 30 days by 200 workers working 24 hours per day. Determine the number of people in a new team that works 16 hours a day and completes the task in 24 days.

The three parameters in question are the number of workers, the number of hours, and the number of days.

Amount one is inversely proportional to quantity two, and quantity two is also inversely proportional to quantity three.

The following formula can be used to calculate compound ratio.

The number of employees in the recruited team is equal to 

200×24×3224×16

•                  400 workers

The total number of workers that new company recruits is 400 workers.

Examples of compound ratio

• What is the compound ratio of 20:30 and 60:40? 

The compound ratio of 20:30 and 60:40 is

Given ratio is in the form of a:b and c:d which can be equalizes to ac:bd.

In the given problem, a is 20, b is 30, c is 60, d is 40

• ac : bd
• (a ×c :b×d)
• (20 ×60 :30 ×40)
• (120 : 120)
• (1 : 1)

The compound ratio of 20:30 and 60:40 is 1:1.

The compound ratio of two terms like a: b and c : d is ac: bd.

Similarly, The compound interest of a:b, c:d, e:f can be ace : bdf.

Meanwhile, The compound interest of a:b,c:d,e:f,l:m can be acdl : bdfm.

Example 2:

The compound ratio of 4:3 and the ratio of 5:4 is 45: x. Find x.

Note:  For two ratios a:b and c:d then the compound ratio is ac:bd

Step by step process

Now, we know that Compound ratio is;
a:bandc:d=ac:bd
Where a:b = 3:4 and c:d = 5:4
3:4 and 5:4=45:x
⇒3×5:4×4=45:x (here we multiply a X c and b X d)
⇒15:16=45:x
Now, we will solve this equation for x
15/16=45/x
⇒15×x=16×45
x=16×45/15=48

Therefore, the value of x is 48 and the ratio is 45:48

Example 3

 Find the compound ratio of the following ratios. 4 : 6 and 8 : 15?

Hint : For two ratios a:b and c:d then the compound ratio is ac:bd

Step by step solution:

Given a is 4, b is 6, c is 8, d is 15

• abcd
• 46815
• 15×4 :8×6
• 60:48
• 5:4

Therefore, the compound ratio of 4 : 6 and 8 : 15 is 5:4.

Example 4:

What is the compound ratio of the given ratios 5:6 and 10:12

Step by step solution:

Note: For two ratios a:b and c:d then the compound ratio is ac:bd

In the given problem, a is 5, b is 6, c is 10, d is 12.

Compound ratio is 561012

• 50:72
• 25:36

Therefore, the compound ratio of the given ratios 5:6 and 10:12 is 25:36.

Example 5

What is the compound ratio of the given ratio (m – n):(m + n),(m+n)2🙁m2+n2)and m4–n4🙁m2–n22)?

Note: For two ratios a:b and c:d then the compound ratio is ac:bd

Step by step solution:

Compound ratio can be written as Product of antecedentsproduct of consequents

The given problem can also be written as

=> (m – n)(m + n) and (m+n)2(m2+n2) and m4–n4(m2–n22)

Calculating further we will get

• (m – n)(m + n)m+n m+n (m2+n2)m2+n2 m+n(m-n)(m+n)2(m-n)2

Whose result is 1.

Therefore, the compound ratio of the given ratio (m – n):(m + n),(m+n)2🙁m2+n2)and m4–n4🙁m2–n22) is one.

Example 6:

Find the compound ratio of mx:l2 and m2:xl  ?

Note:  For two ratios a:b and c:d then the compound ratio is ac:bd

 Step by step solution:

Compound ratio can be written as Product of antecedentsproduct of consequents

The given problem can also be written as a=mx, b = l2 , c = m2, d = xl

Then we have formulae, ac:bd which is 

• (mx . m2) : (l2 .  xl)
• m3x 😡l3 = ac:bd

Therefore, the compound ratio of mx:l2 and m2:xl is m3x 😡l3.

    In the above problem, the terms a and c are the antecedents and the resultant term ac is the antecedent. And the terms b and d are consequents and the resultant term bd is the consequents.

Conclusion

Compound ratio is a concept of ratio concept, which makes over life easier by calculation with simple equations. To calculate compound ratio the formulae we use is the product of antecedents: product of consequents.