Are you searching for the word problems on ratio, this page helps you to get answers to your questions. Here, students or teachers can get many types of ratios word problems which helps to understand the concept thoroughly. The word ‘Ratio’ is a term used to compare two or more numbers or quantities.
By using ratio it is very simple to solve the problems and gives the result in the simplest form. We use ‘:‘ to denote the ratio while comparing the quantities and read as ” is to “. Let us practice some examples from this ratio word problems worksheet with answers pdf and get an idea of how to solve the problems on ratio.
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Ratio Word Problems with Solutions
Example 1:
Find the quantity if it is divided in the ratio 6: 4, the smaller part is 48.
Solution:
Let the quantity be ‘m’.
Then the ratio of two parts is written as \(\frac{6m}{6+4}\) and \(\frac{4m}{6+4}\).
Here, the smaller part is 48, we get
\(\frac{4m}{6+4}\) = 48
⇒ \(\frac{4m}{10}\) = 48
⇒ 4m = 48×10
⇒ 4m = 480
⇒ m = \(\frac{480}{4}\)
⇒ m = 120
Therefore, the quantity is 120.
Example 2:
A herd of 50 cows and buffaloes has 14 cows and some buffaloes. What is the ratio of buffaloes to cows?
Solution:
Given a total of 50 cows and buffaloes.
There are 14 cows given.
To get the count of buffaloes = 50 – 14 = 36.
The ratio of buffaloes to cows is 36: 14 = 18: 7.
Hence, the simplest form of ratio is 18: 7.
Example 3:
Mr. Ram’s class has 40 students, of which 18 are girls. Find the ratio of girls to boys?
Solution:
Total students in a class = 40.
No. of girls in a class = 18 (given)
No. of boys in a class = Total students – No. of girls = 40 – 18 = 22.
There are 22 boys in a class.
The ratio of girls to boys is 18: 22.
Here, there is a common factor 2. So, we can write the ratio in the simplest form by dividing it with the factor 2.
The simplest form of ratio is 9: 11.
Example 4:
If the ratio of p: q = 4: 3, then find (2p- 3q) : (5p+q)?
Solution:
Given p: q = 5: 3, then p = 5m and q = 3m (m ≠ 0 is a common multiplier).
Now, (2p- 3q) : (5p+q) = \(\frac{2p-3q}{5p+q}\)
= \(\frac{(2×5m)-(3×3m)}{(5×4m)+3m}\)
= \(\frac{10m-9m}{20m+3m}\)
= \(\frac{1m}{23m}\)
= \(\frac{1}{23}\)
= 1: 23.
Therefore, the ratio (2p- 3q) : (5p+q) = 1: 23.
Example 5:
Two numbers are in the ratio 3: 4. If 3 is added to the first number and 8 is added to the second number, they are in the ratio of 3: 5. Find the numbers?
Solution:
Given the ratio of two numbers is 3: 4.
Let the numbers be 3x and 4x.
According to the problem given,
\(\frac{3x+3}{4x+8}\) = \(\frac{3}{5}\)
⇒ 5(3x+3) = 3(4x+8)
⇒ 15x+15 = 12x+24
⇒ 15x-12x = 24-15
⇒ 3x = 9
⇒ x = \(\frac{9}{3}\)
⇒ x = 3.
Hence, the original numbers are 3x = 3×3 = 9 and 4x = 4×3 = 12.
Therefore, the numbers are 9 and 12.
Example 6:
Find the ratio of a: c from the quantities a: b = 4: 5, b: c = 2: 6?
Solution:
Given the ratios a: b = 4: 5, b: c = 2: 6.
a: b = 4: 5 ⇒ \(\frac{a}{b}\) = \(\frac{4}{5}\) ——(i)
b: c = 2: 6 ⇒ \(\frac{b}{c}\) = \(\frac{2}{6}\) ——(ii)
Now, multiply the equations (i) and (ii), we get
\(\frac{a}{b}\) × \(\frac{b}{c}\) = \(\frac{4}{5}\) × \(\frac{2}{6}\)
⇒ \(\frac{a}{c}\) = \(\frac{8}{30}\)
The ratio a: c = 8: 30 = 4: 15.
Thus, the ratio a: c = 4: 15.
Example 7:
If we have the ratio of tomatoes to apples is 2: 4. If there are 18 tomatoes. How many apples are there?
Solution:
The ratio of tomatoes to apples is 2: 4 means that for every 2 tomatoes, you have 4 apples.
Here, you have 18 tomatoes, or we can say 9 times as much.
So, you need to multiply the apples by 9.
⇒ The apples we have is 4 = 4 × 9 = 36.
Thus, there are 36 apples.
Example 8:
If the equation (2x+5y): (6x-4y) = 8: 5. Find the ratio of x: y?
Solution:
Given, (2x+5y): (6x-4y) = 8: 5
Now,
\(\frac{2x+5y}{6x-4y}\) = \(\frac{8}{5}\)
⇒ 5(2x+5y) = 8(6x-4y)
⇒ 10x+25y = 48x-32y
⇒ 10x – 48x = -32y – 25y
⇒ -38x = -57y
⇒ 38x = 57y
⇒ \(\frac{x}{y}\) = \(\frac{57}{38}\)
⇒ x: y = 57: 38.
Hence, that ratio of x: y is 57: 38.
Example 9:
Manoj leaves $ 2461600 behind. Manoj’s wish was the money is to be divided between his son and daughter in the ratio of 3: 2. Find the money received by his son and daughter?
Solution:
Manoj has money of $ 2461600 and is to be shared with his son and daughter in the ratio of 3: 2.
We know if a quantity x is divided in the ratio of a: b, then the two parts are look alike. i.e., \(\frac{ax}{a+b}\) and \(\frac{bx}{a+b}\).
Now, the money received by his son = \(\frac{3}{3+2}\) × $ 2461600
= \(\frac{3}{5}\) × $ 2461600
= 3 × $ 492320
= $ 1476960
Next, the money received by his daughter = \(\frac{2}{3+2}\) × $ 2461600
= \(\frac{2}{5}\) × $ 2461600
= 2 × $ 492320
= $ 984640
Thus, the money received by Manoj’s son is $ 1476960 and by his daughter is $ 984640.