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Introduction to Ratio and Proportions:
Ratio:
The ratio of two quantities a and b in the same units, is the fraction and we write it as a : b.
In the ratio a : b, we call ‘a’ as the first term or antecedent and ‘b’, the second term or consequent.
Eg. The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent = 9.
Proportion:
Proportions is where two ratios are compared and equated.
Where a:b is a ratio and c:d is another ratio, and if they are equal,
then, they can be rewritten as a:b :: c:d. { the ‘::’ sign means ‘equal to’}
Therefore, a:b = c:d
Properties of proportions:
(i) a:b = c:d
can be written as a/b = c/d
which implies, axd = bxc, or, ad = bc
this property helps in solving many questions
(ii) if a:b = b:c, which means this proportions between three numbers is in the form of
‘continued proportions’, as all three numbers are having a connection.
so, a/b=b/c or,
ac=bxb or,
ac=b2
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Question 1 of 15
1. Question
If a:b = 2:3 and b:c = 4:3, then find a:b:c
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Question 2 of 15
2. Question
If A:B:C = 2:3:4, then find
AB:BC:CACorrect
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Question 3 of 15
3. Question
If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D
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Question 4 of 15
4. Question
If 2 : 9 :: x : 18, then find the value of x
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Question 5 of 15
5. Question
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
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Question 6 of 15
6. Question
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?
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Question 7 of 15
7. Question
Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
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Question 8 of 15
8. Question
In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is:
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Question 9 of 15
9. Question
Find the mean proportional of 4 and 36.
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Question 10 of 15
10. Question
In a certain room, there are 28 women and 21 men. What is the ratio of men to women? What is the ratio of women to the total number of people?
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Question 11 of 15
11. Question
If the ratio of chocolates to icecream cones in a box is 5:8 and the number of chocolates is 30, find the number of icecream cones.
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Question 12 of 15
12. Question
A certain recipe calls for 3kgs of sugar for every 6 kgs of flour. If 60kgs of this sweet has to be prepared, how much sugar is required?
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Question 13 of 15
13. Question
There is a 20 litres of a solution which has 20% of bleach. Extra bleach is added to it to make it to 50% bleach solution. How much water has to be added further to bring it back to 20% bleach solution?
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Question 14 of 15
14. Question
If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)
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Question 15 of 15
15. Question
if x:y = 1:3, then find the value of
(7x+3y):(2x+y)Correct
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