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Unit 3

Q1. Find the fourth proportional to the numbers 3,4,5.

(a) 20 (b) 10 (c) 15 (d) 5

Solution.
2:4 = 5:x

2 x (x) = 4 x 5

x = 20/2 = 10
Solution

Q2. Find the mean proportional between 25 and 9.

(a) 20 (b) 15 (c) 16 (d) 18

Solution.
25 : x = x : 9

x2 = 225

x = 15
Solution

Q3. A mixture contains milk and water in the ratio 8:3, on adding 3 litre of water , the ratio of milk to water becomes 2:1 . find the quantity of milk in the mixture .

(a) 24 litre (b) 15 litre (c) 20 litre (d) 25 litre

Solution.
M/W = 8/3,

M/(W + 3) = 2/1 ,

M = 2W + 6

M = 2(3M/8) + 6

8M = 6M + 48

2M = 48

M = 24
Solution

Q4. If the sides of a rhombus are increased by 10%, what is the increase in its area ?

(a) 21% (b) 12% (c) 40% (d) 10%

Solution.
= (2x + x2/100)%

= 20 + 100/100

= 21%
Solution

Q5. Which statement is true . (1) In simple partnership capitals of the partners are invested for the same period.
(2) In compound partners are invested for the different span of time.

(a) only 1 (b) only 2 (c) both (d) none of these

Solution.
(c) both
Solution

Q6. x,y and z invested capitals in the ratio 7:6:6 . At the end of one year they received profits in the ratio 7:3:9. Find the ratio of time contributed their funds .

(a) 2:1:3 (b) 1:2:2 (c) 3:2:1 (d) 4:3:2

Solution.
(a) 2:1:3
Solution

Q7. The average of 15 numbers is 36, if all numbers are increased by 36 then the new average of 15 numbers will be .

(a) 72 (b) 70 (c) 36 (d) 18

Solution.
(a) 72
Solution

Q8. In a class , there are 20 boys and 30 girls having average marks in maths and stats 30 and 20 respectively . find the average of whole class.

(a) 32 (b) 30 (c) 24 (d) 28

Solution.
(c) 24
Solution

Q9. The age of the father 3 years ago was 7 times the age of his son. At present the father's age is 6 times that of his son . find the age of son ?

(a) 18 (b) 20 (c) 21 (d) 25

Solution.
(a) 18
Solution

Q10. The ratio of the father's age to the son's is 3:1 . The product of their ages 27, find the age of son ?

(a) 6 (b) 3 (c) 2 (d) 1

Solution.
Let the ratio of proportionality be y,then

3y . y = 27

3y2 = 27

y2 = 9

y = 3
Solution