Ratio and Rate of Work


A ratio is a comparison of two quantities with same unit

For example, suppose there are 10 boys and 15 girls in a classroom. One way, not to compare these quantities would be to say that there are 5 more girls than boys in the classroom. However to say in terms of ratio, we say that the ratio of boys to girls is 10 to 15, or 2 to 3. In other words, for every 2 boys in the classroom, there are 3 girls.

You can express a ratio using a colon or a fraction, as 10 boys : 15 girls, or 10 boys/15 girls. The fraction notation is usually superior for ratios with two elements, but if you have a ratio with three elements, then the colon notation is usually superior: for example, 10 : 15 : 19.

In the classroom example, many other ratios can be made. The number of boys out of the total number of students is 10/25.The number of girls out of the total number of students is 15/25.And 15/10 is the ratio of the number of girls to the number of boys.

Ratios, being fractions, can sometimes be reducible. For example, the ratio of boys to

girls in our hypothetical classroom is 10/15. So, we would be correct if we said that the ratio of boys to girls in our hypothetical classroom is 2 : 3, or two boys for every 3 girls.

Notice that knowing a ratio doesn’t tell us the actual numbers involved. If the ratio

of boys to girls is 2:3 or 2/3, we don’t know whether the actual number of boys and girls is 2 and 3, 10 and 15, or 200 and 300.

Let’s do few problems on ratios.


If a:b = 2:3 ; b:c=3:4 ; c:d=8:9 and d:e = 27:12, then what is the ratio of a:b:c:d:e ?


 a:b = 2:3 and b:c = 3:4. Hence, a:b:c = 2:3:4

 c:d = 8:9 and d:e = 9:4. Hence, c:d:e = 8:9:4 

With a:b:c = 2:3:4   and c:d:e = 8:9:4, the common term is c in both the case, therefore  we multiply the first one by 2. So the new one looks like a:b:c  = 4, 6,8

Combining the ratio

a:b:c:d:e =4 :6:8:9:4


A company’s profits obtained from Product A, Product B, and Product C are in the ratio 47:1:2, respectively. If the total profits from these three products is $16,000, what is the profit from Product C?

A. $1,610   B. $1,290 C. $960   D. $640  E. $320


Convert the values in terms of multipliers.

Then,  A = 47x, B= x, C = 2x 

Hence, A+B+C = 47x + x + 2x = 50x 

Now as per the question, 50x = 16000

or, x = 1600050=320 

Therefore , Profit from C = 2x= 2 x 320 = 640

And, right answer is Option (D)


Work done or rate of work involves questions on a number of people or machines working together to complete a task. We are usually given individual rates of completion. And, we are asked to find out how long it would take if they work together. Sounds simple enough doesn’t it? Well it is!

There is just one simple concept we need to understand in order to solve any work

related word problem. We shall understand this using the following example:

Example: A, B, and C, required to make wall. A alone can completely built the wall

in 10 days, B alone can do it in 15 days and C can do it in 30 days. If all of them worked

together in how may days the wall will be done?


Step 1: We take the total as the L.C.M of the given values. The L.C.M will be 30 units.

Step 2: We calculate how much work each person/machine does in one unit of time (could be days, hours, minutes, etc). Here,

A does the job of 30 units in 10 days, so in one day he will do = 30/10 = 3 units / day

A does the job of 30 units in 15 days, so in one day he will do = 30/15 = 2 units / day

A does the job of 30 units in 30 days, so in one day he will do = 30/30 = 1 unit / day

Step 3: We add up the amount of work done by each person/machine in that one unit of

time. This would give us the total amount of work completed by both of them in one day

= 3+2+1 = 6 units

Step 4: We calculate total amount of time taken for work to be completed when all

persons/machines are working together. The approach is similar to one we used in STEP 2, the only difference being that we use it in reverse order. Here it would be 6 units of work is done in 1 day. 1 unit of work is done in 1/6 day. So 30 units of work is done in 1/6 x 30 = 5 days

Hence, the answer is 5 days.

Here, once we understand the logic in the above steps, we will have all the

information we need to solve any work related word problem. We will see that the

formula we might have come across, can be very easily and logically deduced from this concept.

Leave Comment

Your email address will not be published. Required fields are marked *