Ratio, Proportion & Partnership: Exercise Problem & solved examples

Question: 1 The ratio of 1/5 to 2/7 is:
Option: (a) 3:5 (b) 5:7 (c) 7:9 (d) 7:10 (e) 3:7

Explore: The ratio of 1/6 to 2/7
= 1/5:2/7
= (1/5)/()2/7
= 1/5 x 7/2
= 7/10
= 7: 10
Answer: (d)

Question: 2 The ratio of 1/4 to 3/5 is
Option: (a) 1 to 3 (b) 3 to 20 (c) 5 to 12 (d) 3 to 4 (e) 5 to 5

Explore: 1/4 to 3/5 = 1/4:3/5 = (1/4)/(3/5) = 5/12
Answer: (c)

Question: 3 A:B = 4:5, A:C = 10:9, then A:B:C = ?
Option: (a) 4:5:9 (b) 4:5:10 (c) 8:9:10 (d) 8:9:10 (e) 20:25:18

Explore: A:B = 4:5
=> B:A = 5:4
=> B:A = 5:5 x 4:5 = 25:20
A:C = 10:9
=> A:C = 10x2:9x2 = 20:18
:. B:A:C = 25:20:18
:. A:B:C = 20:25:18
Answer: (e)

Question: 4 If A:B = 1:2, B:C = 4:3, & A+B+C = 450. What is the value of B?
Explore: A:B = 1:2 = 1x2:2x2 = 2:4
B:C = 4:3
:.  A:B:C = 2:4:3
Sum of the numbers = 2+4+3 = 9
:. Value of B = 450x(4/9) = 200
Answer: 200

Question: 5 Let, X:Y = 3:4 and X:Z = 6:5, then Z:Y =?
Option: (a) 5:3 (b) 6:7 (c) 4:2 (d) 5:4 (e) 5:8

Explore: X:Y = 3:4
=> Y:X = 4:3 => Y:X = 4x2:2x3 = 8:6
Again, X:Z = 6:5
:. Y:X:Z =8:6:5
:. Z:Y = 5:8
Answer: (e)

Question: 6 If X:Y = Y:Z = 1.5 and Z = 2, what is the value of X?
Option: (a) 3 (b) 4 (c) 4.5 (d) 2.5 (e) 5

Explore: Y:Z = 1.5 or Y/Z = 1.5
Or, Y = 1.5Z = 1.5x2 = 3
Now, Z:Y = 1.5
:. X = 1.5Y = (3/2)3 = 9/2 = 4.5
Answer: (c)

Question: 7 If X is 2/5 of Y and Y is 5/7 of Z, what is the ratio of Z:X?
Explore: According to the question,
X = 2Y/5 & Y = 5Z/7
=> X = 2/5 x 5Z/7
=> X = 2Z/7
=>Z/X = 7/2 = 7:2
Answer: 7:2

Question: 8 In a school, the ratio of boys to girls is 3 to 7. If there are 150 boys and girls in the school, how many boys are there?
Option: (a) 45 (b) 75 (c) 90 (d) 105

Explore: The ratio of boys to girls = 3:7
Sum of the ratio = 3 + 7 = 10
No. of boys = 150 x 3/10 = 45
Answer: (45)

Question: 9 The ratio of girls to boys in a class is 3:4. The number of students in the class could be any of the following except:
Option: (a) 35 (b) 28 (c)48 (d) 42

Explore: Since ratio of girls to boys is 3:4 and no. of student can't be fraction and must be divisible by 7(3+4), so, 35, 28 & 42 are divisible by 7.
But 48 is not divisible by 7.

Posted in: Exercise Problem, Exercise(Ratio & Proportion), Partnership, Proportion, Ratio, Solutions to Problems