Worksheet on Ratio of Two or More Quantities gives information of ratio in different types and quantities. The ratio indicates their relative sizes and always expresses the ratio numbers in the lowest terms possible. A ratio compares two or more different quantities that have the same units of measure. In this ratio of two or more quantities word problems worksheet pdf, students can get the questions that are relevant to how to divide a quantity into two parts or more than the quantities of a given ratio with detailed solutions.

Practice with these activity sheet questions to have the hold on the concept of a ratio if we have more than two quantities of the same kind. This free printable activity sheet on the Ratios of two or more quantities is a fun-learning workbook to solve all the questions. Also, students can able to create the questions themselves in different types by using this ratio of two or more quantities worksheet.

Do Check: Worksheet on Ratios

## Sharing a Quantity in Given RatioWorksheet with Answers PDF

**Example 1:**

Find p: s, if p: q = 4: 6 and r: s = 3: 12.

**Solution:**

Given ratios are p: q = 4:6 and r: s = 3: 12

Now, to find the ratio of p: s.

As we know, if there is a ratio of quantities a: b and c: d. To get a: d = \(\frac{a}{b}\) × \(\frac{c}{d}\) = \(\frac{a}{d}\).

Similarly, we apply the same formula

p: s = \(\frac{p}{q}\) × \(\frac{r}{s}\)

⇒ p: s = \(\frac{4}{6}\) × \(\frac{3}{12}\)

⇒ p: s = 1: 6

Therefore, the value of the ratio p: s is **1: 6**.

**Example 2:**

If x: y = 5: 4 and y: z = 2: 6, then find (i) x: z and (ii) x: y: z.

**Solution:**

(i) Given x: y = 5: 4 and y: z = 2: 6

To get x: z, we use the formula, x: z = \(\frac{x}{y}\) × \(\frac{y}{z}\)

So,

x: z = \(\frac{5}{4}\) × \(\frac{2}{6}\)

⇒ x: z = \(\frac{5×2}{4×6}\)

⇒ x: z = \(\frac{10}{24}\)

⇒ x: z = \(\frac{5}{12}\)

Thus, the ratio x: z = **5: 12**.

(ii) Given ratio x: y = 5: 4 and y: = 2: 6

Now, to find the ratio of x: y: z.

Here, the values of y are not the same. To get the ratio of x: y: z, we have to multiply the value of y with a number to get both the values equal.

\(\frac{x}{y}\) = \(\frac{5}{4}\) × \(\frac{1}{1}\) = \(\frac{5}{4}\)

\(\frac{y}{z}\) = \(\frac{2}{6}\) × \(\frac{2}{2}\) = \(\frac{4}{12}\)

Thus, the ratio x: y: z = **5: 4: 12**.

**Example 3:**

Divide ₹ 3876 in the ratio \(\frac{4}{5}\): 1\(\frac{3}{5}\).

**Solution:**

Given ratio \(\frac{4}{5}\): 1\(\frac{3}{5}\) i.e., \(\frac{4}{5}\): \(\frac{8}{5}\).

Therefore, the ratio becomes 4: 8 = 4+8 = 12.

Let the common multiple be x.

12x = 3876

x = \(\frac{3876}{12}\)

⇒ x = 323

Now, 4x = 4×323 = 1292

8x = 8×323 = 2584

Thus, the ratio is divided into **₹1292** and **₹2584**.

**Example 4:**

If a: b = 3: 7, then find the ratios of the following:

(i) (2a+ 5b): (3a+ 6b)

(ii) (a+ 2b): (7a- b)

**Solution:**

(i) Given ratio a: b = 3: 7

The given equation is (2a+ 5b): (3a+ 6b).

Now, substitute the values of a and b in the above equation.

(2a+ 5b): (3a+ 6b) = ((2×3)+(5×7)): ((3×3)+(6×7)) = (6+35): (9+42) = 41: 51

Thus, the ratio of the equation (2a+ 5b): (3a+ 6b) is **41: 51**.

(ii) Given equation is (a+ 2b): (7a- b)

The values of a and b were given are 3 and 7.

Now, substitute the values in the above equation.

(a+ 2b): (7a- b) = (3+(2×7)): ((7×3)-7) = (3+14): (21-7) = 15: 14

Hence, the ratio is **15: 14**.

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**Example 5:**

Find the value of m, if (m-1): (m+3) is the reciprocal ratio of 12: 8.

**Solution:**

The reciprocal ratio of 12: 8 is 8: 12.

Now, 8: 12 = (m-1): (m+3)

⇒ \(\frac{8}{12}\) = \(\frac{m-1}{m+3}\)

⇒ 8(m+3) = 12(m-1)

⇒ 8m+24 = 12m-12

⇒ 8m- 12m = -12 – 24

⇒ -4m = -36

⇒ m = \(\frac{36}{4}\)

⇒ m = 9.

Therefore, the value of m is **9**.

**Example 6:**

If 4x = 7y = 2z, find the ratio of x: y: z.

**Solution:**

Given equation is 4x = 7y = 2z.

Now, 4x = 7y

⇒ x = \(\frac{7y}{4}\) —- (i)

7y = 2z

⇒ z = \(\frac{7y}{2}\) —- (ii)

Now,

x: y: z = \(\frac{7y}{4}\): y : \(\frac{7y}{2}\) (from (i) and (ii))

⇒ x: y: z = \(\frac{7}{4}\): 1 : \(\frac{7}{2}\)

⇒ x: y: z = 7: 4: 14

Hence, the ratio of x: y: z is **7: 4: 14**.

**Example 7:**

Divide $ 3570 in the ratio \(\frac{1}{5}\): 1\(\frac{2}{3}\): \(\frac{2}{15}\).

**Solution:**

Given ratio is \(\frac{1}{5}\): 1\(\frac{2}{3}\): \(\frac{2}{15}\) i.e., \(\frac{1}{5}\): \(\frac{5}{3}\): \(\frac{2}{15}\).

Let the common multiple be k.

Therefore, \(\frac{1k}{5}\): \(\frac{5k}{3}\): \(\frac{2k}{15}\) = 3570

⇒ \(\frac{3k}{15}\): \(\frac{25k}{15}\): \(\frac{2k}{15}\) = 3570

⇒ \(\frac{30k}{15}\) = 3570

⇒ 2k = 3570

⇒ k = \(\frac{3570}{2}\)

⇒ k = 1785

Now, to find the three equal ratios

\(\frac{1k}{5}\) = \(\frac{1×1785}{5}\) = \(\frac{1785}{5}\) =357

\(\frac{5k}{3}\) = \(\frac{5×1785}{3}\) = \(\frac{8925}{3}\) = 2975

\(\frac{2k}{15}\) = \(\frac{2×1785}{15}\) = \(\frac{3570}{15}\) = 238

The ratio is divided into **$357**, **$2975**, and **$238**.

**Example 8:**

If a: b = 4: 1, b: c = 12: 7, and c: d = 7: 9, then find the triplicate ratio of a: d.

**Solution:**

Given ratios are a: b = 4: 1, b: c = 12: 7, and c: d = 7: 9

Now, to find the ratio of a: d.

Here,

a: d = \(\frac{a}{b}\) × \(\frac{b}{c}\) × \(\frac{c}{d}\)

⇒ a: d = \(\frac{4}{1}\) × \(\frac{12}{7}\) × \(\frac{7}{9}\)

⇒ a: d = \(\frac{4×12×7}{1×7×9}\)

⇒ a: d = \(\frac{4×4×1}{1×1×}\)

⇒ a: d = 16: 3

The ratio of a: d is 16: 3.

Triplicate ratio = 16³ : 3³ = 4096 : 27.

Therefore, the triplicate ratio of a: d = **4096: 27**.

**Example 9:
**What number should be added to the ratio of 13: 33? So, the ratio becomes 4: 9.

**Solution:**

Given ratio is 13: 33

Now, we have to add the number so that we can get the ratio of 4: 9.

If we add the number 3 to the ratio of 13: 33

We got, 13+3: 33+3 = 16: 36.

So, the ratio becomes 16: 36 = 4: 9.

Thus, the number **4** should be added to the given ratio.