**Ratio and Proportions problems and solutions**

**What is a ratio?**

A ratio is a representation of distribution of a value present among the persons present and is shown as follows:

If a total is divided among A, B and C such that A got 4 parts, B got 5 parts and C got 6 parts then it is represented in ratio as A:B:C = 4:5:6.

So, 4:5:6 means that the total value is divided into 4+5+6 = 15 equal parts and then distributed as per the ratio.

**Example 1:**

Divide Rs. 580 between A and B in the ratio of 14:15.

**Soln:**

A:B = 14:15 => 580 is divided into 29 equal parts => each part = Rs. 20.

So A’s share = 14 parts = 14 x 20 = Rs. 280

B’s share = 15 parts = Rs. 300.

**Example 2:**

If A:B = 2:3 and B:C = 4:5 then find A:B:C.

**Soln:**

To combine two ratios the proportions common for them shall be in equal parts. Here the common proportion is B for the given ratios.

Making B equal in both ratios they become 8:12 and 12:15 => A:B:C = 8:12:15.

**Example 3:**

Three numbers are in the ratio of 3: 4 : 8 and the sum of these numbers is 975. Find the three numbers.

**Soln:**

Let the numbers be 3x, 4x and 8x. Then their sum = 3x+4x+8x = 15x = 975 => x = 65.

So the numbers are 3x = 195, 4x = 260 and 8x = 520.

**Example 4:**

** **

Two numbers are in the ratio of 4 : 5. If the difference between these numbers is 24, then find the numbers.

**Soln:**

Let the numbers be 4x and 5x. Their difference = 5x – 4x = x = 24 (given).

So the numbers are 4x = 96 and 5x = 120.

**Example 5:**

Given two numbers are in the ratio of 3 : 4. If 8 is added to each of them, their ratio is changed to 5 : 6. Find two numbers.

**Soln:**

Let the numbers be a and b.

A:B = 3:4 => A / B = 3 / 4.

Also, (A+8) / (B+8) = 5 / 6.

Solving we get, A=12 and B = 16

**Example 6:**

** **

A garrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers will join the group. For how many more days will the provisions last?

**Soln:**

Actually after 180 days,

If 120 members are there provisions come for 60 more days (since total 240 days)

But now 180 members are there.

So number of days = (120/180) X 60 = 40 days.

**Example 7:**

** **

If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it?

**Soln:**

24 men – 12 hrs – 16 days

8 men – 6 hrs – ? days (n)

n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional)

=> n = 96 days.

murial says

thanks babes

babitha says

thanku you so much..now problem solving became much easier than before…………interesting………nice job syed……………

Anuj says

heyy pls giv details om the 6th sum m finding sums of this type really hard 🙁