Ratio & Proportion

In this section we will have Maths Aptitude Questions related to Ratio & Proportion. Aptitude Problems on this topic are asked frequently in all competitive and Entrance exams.

We have listed few important formulas/facts which will come handy in solving questions related to Ratio & Proportion.

Ratio & Proportion Tips

  • Ratio -.In the ratio a:b, “a” is called as the first term or antecedent and b, the second term or consequent.
  • Proportion – The equality of two ratios is called proportion. Eg. a:b = c:d is equivalent to a:b::c:d and it means a,b,c and d are in proportion.
  • In equation a:b::c:d , a and d are called extremes and b and c are called mean terms.
  • Product of means = Products of Extremes i.e. a:b::c:d <> (b x c) = (a x d)
  • Fourth Proportional – If a:b ::c:d , then d is called fourth proportional to a,b and c.
  • Third Proportional – If a:b ::b:c , then c is called third proportional to a and b
  • Mean Proportional – Mean proportional between a and b is \( \sqrt{ab} \)
  • Compounded ratio – The compounded ratio of the ratios (a:b) , (c:d), (e:f) is (ace:bdf)
  • If (a/b) = (c/d) then (a+b)/(a-b) = (c+d)/(c-d)

Lets get started with some real life problems !!

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Ratio & Proportion Maths Aptitude Question – Test series

Q 1 – A person spends Rs 8100 in buying some tables at Rs 1200 each and some chairs at Rs 300 each. The ratio of the number of chairs to that of the tables when the maximum possible number of tables is purchased ?
  • 1 : 2
  • 1 : 4
  • 2 : 1
  • 5 : 7

Q 2 – Which of the following represents ab = 64 ?
  • 8 : a = 8 : b
  • a : 16 = b : 4
  • a : 8 = b : 8
  • 32: a = b : 2

Q 3 – In a proportion, the product of 1st and 4th terms is 40 and that of 2nd and 3rd terms is 2.5x. Then the value of x is ..?
  • 16
  • 26
  • 75
  • 90

Q 4 – If 20% of A = 30% of B = 1/6 th of C, then A:B:C is .. ?
  • 2 : 3 : 16
  • 3 : 2 : 16
  • 10 : 15 : 18
  • 15 : 10 : 18

Q 5 – If A:B = 2:3 and A:C = 1:2 , then what is B:C ?
  • 3 : 4
  • 4 : 3
  • 2 : 3
  • 4 : 5

Q 6 – If A:B = 2:3 , B:C = 2:4 and C:D = 2:5 then A:D will be equal to .. ?
  • 1 : 5
  • 2 : 5
  • 3 : 5
  • 2 : 15

Q 7 – If a:(b+c) = 1:3 and c:(a+b) = 5:7 , then b:(a+c) is equal to .. ?
  • 1 : 2
  • 2 : 3
  • 2 : 1
  • 1 : 3

Q 8 – If p:q:r = 2:3:4 and 2p – 3q + 4r = 33 then the value of r is ?
  • 6
  • 9
  • 12
  • 15

Q 9 – Find the two numbers whose mean proportion is 12 and third proportional is 324 ?
  • 6 and 8
  • 4 and 36
  • 3 and 24
  • 8 and 32

Q 10 – When 30% of one number is subtracted from another number, the second number reduces to its four-fifths. What is the ratio of first to second number ?
  • 2 : 5
  • 3 : 2
  • 4 : 7
  • None of the above

Q 11 -One-fourth of sixty percent of a number is equal to two-fifths of twenty percent of another number. What is the respective ratio of the first number to the second number ?
  • 4 : 7
  • 5 : 9
  • 8 : 15
  • None of the above

Q 12 – 5 Mangoes and 4 Oranges cost as much as three Mangoes and seven Oranges. What is the ratio of cost of 1 Mango to 1 Orange?
  • 4 : 3
  • 1 : 3
  • 3 : 2
  • 4 : 3

Q 13 – Joy and David divide a sum of $25000 in the ratio of 3:2 respectively. If 5000 is added to to each of their shares, what would be the new ratio formed ?
  • 2 : 3
  • 3 : 4
  • 5 : 4
  • 4 : 3

Q 14 – The numbers x,y,z are proportional to 2,3,5. the sum of x,y,z is 100. if y = px – 10, then p is equal to ..?
  • 3/2
  • 2
  • 5/2
  • 3

Q 15 – An amount of 53 is divided among A,B and C such that A gets 7 more than B and B gets 8 more than C. What is the ratio of their shares ?
  • 15:8:30
  • 16:9:18
  • 18:25:10
  • 25:18:10

Q 16 – A sum of Rs 731 is divided among A,B and C such that A receives 25% more than B and B receives 25% less than C. What is C’s share in the amount ?
  • 172
  • 200
  • 272
  • 282

Q 17 – A person distributes his pens among four friends A,B,C and D in the ratio 1/3:1/4:1/5:1/6. What is the minimum number of pens that person should have ..?
  • 23
  • 55
  • 57
  • 65

Q 18 – The sum of the squares of three numbers is 532 and the ratio of the first and the second number as also of the second and third number is 3:2. The third number is .. ?
  • 8
  • 12
  • 18
  • 20

Q 19 – 3 numbers A,B and C are in the ratio of 12:15:25. If the sum of these numbers is 312, than find out what is the ratio between the difference of B and A & the difference of C and B ?
  • 3 : 7
  • 3 : 10
  • 5 : 1
  • 10 : 3

Q 20 – The ratio of number of Boys and Girls in a school of 720 students is 7:5. How many more girls should be admitted in the school to make the ratio 1:1 ?
  • 90
  • 120
  • 220
  • 240

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