Practice the questions given in the worksheet on dividing a quantity in a given ratio. We know, a ratio is a comparison of two or more quantities of the same kind. It can be represented as a fraction. The ratio of P to Q = \(\frac{P}{Q}\) and it is represented as P : Q. The quantities P and Q are called terms: P is the antecedent and Q is the consequent.

**1.** Two numbers are in the ratio 2 : 3, and the sum of the numbers is 225. Find the numbers.

**2.** Divide 275 into two parts which are in the ratio 4 : 7.

**3.** Decrease the number 225 in the ratio 5 : 3.

**4.** A number is divided into two parts in the ratio 4 : 9. If the larger part is 108, find the number.

**5.** Divide 1148 into two parts which are in the ratio 11 : 3.

**6.** A sum of money is divided among A, B and C in the ratio 2
: 5 : 3. B gets $ 125. Find the total amount of money and the amounts that A
and C get.

**7.** Divide 297 into three parts which are in the ratio 5 : 13
: 15.

**8.** A bag contains 1 dollar, 50 cents and 25 cents coins in
the ratio 3 : 5 : 7. The total amount is $ 1856. Find the number of each
denomination.

**9.** A number is divided into three parts in the ratio 2 : 3 :
4. If the largest part 68, find the number and the other parts.

**10.** A number is divided into two parts in the ratio 5 : 3.
If the smaller part is 180, find the number and the larger part.

**11.** The sides of a rectangle are in the ratio 4 : 3. If the
perimeter of the rectangle is 210, find its area.

**12.** The sides of a triangle are in the ratio 2 : 5 : 6 and
its perimeter is 1 m 17 cm. Find the length of the longest side of the
triangle.

**13.** Two numbers are in the ratio 7 : 5. The difference of
the two numbers is 246. Find the numbers.

**14.** Divide 432 into three parts which are in the ratio 1 : 2
: 3.

**15.** The ratio of the shorter sides of a right-angled
triangle is 5 : 12. If the perimeter of the triangle is 420 cm, find the length
of the longest side.

**16.** The ratio of the angles of a triangle is 5 : 7 : 12.
Prove that the triangle is a right triangle.

**17.** The angles of a triangle are in the ratio 3 : 5 : 10.
Find the angles.

**18.** The ratio of the angles of a quadrilateral is 5 : 7 :
12. Find the largest angle of the quadrilateral.

**19.** Find the ratio of the number of boys to the number of
girls in a class if the number of boys is 115 and that of girls is 46.

**20.** The salary of a man was increased in the ratio 7 : 8.
The increased salary was $ 9880. Find his previous salary.

**21.** Three workers worked for 5 hours, 7 hours and 12 hours.
The total wage of $ 13200 was divided among the three workers according to the
number of hours of work they did. How much did each get?

**22.** The weight of two fish tighter is 16 kg. If one fish
weight is 10.5 kg, find the ratio of the weight of the smaller fish to that of
the bigger fish.

**23.** In a cricket match, three batsmen A, B and C together
scored 210 runs in one innings. If the runs scored by them be in the ratio 6 :
7 : 8 respectively then find the runs scored by B.

**24.** The present age of two persons are in the ratio 4 : 3.
Nine years hence their ages will be in the ratio 23 : 18. Find their present
ages.

**25.** The ratio of the pocket money saved by a boy and his sister
is 5 : 4. If the brother saves $ 10 more, how much more the sister should save
in order to keep the ratio of their savings unchanged?

**26.** Two numbers are in the ratio 2 : 3. When 2 is added to the first number and 7 is added to the second number, they are in the ratio 2 : 5. Find the numbers.

**27.** Two numbers are in the ratio 7 : 8. When 5 is subtracted from both numbers, their ratio becomes 2 : 3. Find the numbers.

Answers for the worksheet on dividing a quantity in a given ratio are given below.

**Answers:**

**1.** 90 and 135

**2.** 100 and 175

**3. **135

**4.** 156

**5.** 902 and 246

**6.** $ 250, $ 50, $ 75

**7.** 45, 117, 135

**8.** 1 dollar coin 768, 50 cents coin 1280 and 25 cents coin 1792.

**9.** 153, 34, 51

**10.** 480, 300

**11.** 2700 cm^{2}

**12.** 54 cm

**13.** 861 and 615

**14.** 72, 144, 216

**15.** 182 cm

**17.** 30°, 50° 100°

**18.** 150°

**19.** 5 : 2

**20.** $ 8645

**21.** $ 2750, $ 3850 and $ 6600

**22.** 11 : 21

**23.** 70

**24.** 60 years, 45 years

**25.** $ 8

**26.** 2 and 3

**27.** 7 and 8

● **Ratio and proportion**

**Basic Concept of Ratios****Important Properties of Ratios****Ratio in Lowest Term****Types of Ratios****Comparing Ratios****Arranging Ratios****Dividing into a Given Ratio****Divide a Number into Three Parts in a Given Ratio****Dividing a Quantity into Three Parts in a Given Ratio****Problems on Ratio****Worksheet on Ratio in Lowest Term****Worksheet on Types of Ratios****Worksheet on Comparison on Ratios****Worksheet on Ratio of Two or More Quantities****Worksheet on Dividing a Quantity in a Given Ratio****Word Problems on Ratio****Proportion****Definition of Continued Proportion****Mean and Third Proportional****Word Problems on Proportion****Worksheet on Proportion and Continued Proportion****Worksheet on Mean Proportional****Properties of Ratio and Proportion**

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