**(01)** **How many sides does a regular polygon have whose interior and exterior angles are in the ratio 2:1?**

**Each exterior angle of polygon = 360/n**

**Each interior angle of polygon = ( n – 2 ) × 180 / n**

Thus, ( n – 2 ) × 180 / n : 360/n = 2:1

Thus, n = 6**The regular polygon has 6 sides**

**(02) The ratio of present age of two brothers is 1:2 and 5 years back the ratio was 1:3. What will be the ratio of their age after 5 years?**

Present ages of brothers –> x and 2x

**5 Years back the ratio was 1 : 3**

x – 5 / 2x – 5 = 1 / 3

x = 10

Present ages of brothers – 10 and 20 years,

After 5 years their ages = 15 years and 25 years

Required ratio = 15 : 25 = 3 : 5

**(03) The product of two positive integers is 1575 and their ratio is 9 : 7. The smaller integer is**

First integer = 9x and Second integer = 7x

9x × 7x = 1575

x² = 25, x = 5

Smaller integer => 7x = 7 × 5 = 35

**Hence smaller integer is 35**

**(04) The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally, the total number of students was**

Original Ratio = 2 : 3 : 5

New Ratio = 4 : 5: 7 (when 40 students increased)

Difference in ratio in each class = 2x

This difference arise due to increase in 40 students

Hence, 2x = 40,

==> x = 20

So, number of students in each class = 2(20), 3(20) and 5(20) = 40, 60 and 100

Total number = 40 + 60 + 100 = 200

**(05) The ratio of copper and zinc in brass is 13 : 7. How much zinc will be there in 100 kg of brass?**

Required quantity of zinc => (7/ 13+7) * 100

=>( 7 / 20 ) × 100

=> 35 kg

Hence 35 kg of zinc will be there in 100 kg of brass

**(06) A and B have monthly incomes in the ratio 5 : 6 and monthly expenditures in the ratio 3 : 4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B**

Sol:

Monthly income of A and B be 5x and 6x

Monthly expenditures of A and B be 3y and 4y

5x – 3y = 1800 and 6x – 4y = 1600

Solving above equations; x = 1200 , y = 1400

Income of B = 6x = 6 (1200) = Rs. 7200

**(07) Divide Rs. 7500 among A, B and C such that A’s share to B’s share is in the ratio 5 : 2 and B’s share to C’s share is in the ratio 7 : 13. How much will B receive?**

A : B = 5 : 2

and B : C = 7 : 13,

thus A : B : C = 35 : 14 : 26

Thus, B’s share = 14 / 75 × 7500 = Rs. 1400

**(08) Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is:**

Numbers are 3x, 2x and 5x

Sum of their squares is 1862

(3x)² + (2x)² + (5x)² = 1862

38x² = 1862

x = 7

Smallest number = 2x = 2 (7) = 14

**(09) The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:**

Let the numbers be x. y and z, thus x : y = 2 : 3 and y : z = 5 : 8

Thus, x : y : z = 10 : 15 : 24

y = 15 / 49 × 98 = 30

**Hence the second number is 30**

**(10) A mixture of 30 liters contains milk and water in the ratio of 7 : 3. How much water should be added to it so that the ratio of milk and water become 3 : 7?**

Quantity of milk = 7/10 × 30 = 21 liters, quantity of water = 3/10 × 30 = 9 liters

Let x liters of water should be added

21 / 9 + x = 3 / 7

x = 40 liters

Hence 40 liters of water should be added to make milk to water ratio 3:7