Lesson Examples of Ratio and Proportions

Source code of 'Examples of Ratio and Proportions'

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

Q1. If 4:36::x:63, then find the value of x.
A1. 4:36::x:63
--> {{{1/9=x/63}}}
--> {{{x=63/9}}}
--> x=7

Q2. If a:b = 3:5, b:c = 5:7, c:d = 14:3. Find a:d
A2. {{{a/d = (a/b)*(b/c)*(c/d) = 3/5*5/7*14/3 = 2}}}

Q3. Compare the <a href="ratios.lesson">ratios</a> 3:5 and 2:3.
A3. The LCM of 5 and 3 is 15. 
3:5 = 9:15 
2:3 = 10:15

Since 10:15>9:15, thus 2:3 is greater than 3:5

Q4. If a:b=3:4, b:c=5:7, c:d= 11:13, then compare a,b c and d
A3. a:b = 3:4, therefore a < b
b:c = 5:7, therefore b < c
c:d = 11:13 therefore c < d

Hence a < b < c < d

Q5. The <a href="ratios.lesson">ratio</a> between two quantities is 3:7. If first quantity is 15, find the second one.
A5. Let the second quantity be x.
Thus 3:7 = 15:x
Since Product of Extremes = Product of Means
3x = 15*7 
=> x = 15/3*7 
= 5*7
= 35

Q6. Two numbers are in <a href="ratios.lesson">ratio</a> 3:7. The difference between the numbers is 36. Find the numbers.
A6. Let the numbers be 3x and 7x. Thus the <a href="ratios.lesson">ratio</a> is 3:7. The difference between them would be 7x-3x = 4x. Given that the difference is 36, we get
4x = 36 
=> x = 9
Thus the numbers are 3x and 7x which means 27 and 63.

Q7. Two vessels of equal volume have milk and water in the <a href="ratios.lesson">ratio</a> 3:2 and 3:7. The vessels are then mixed. Find the <a href="ratios.lesson">ratio</a> of milk and water in the mixture.
A7. Let the volume be 1000ml. 
The first vessel would have milk = {{{2/(2+3)*1000 = 2/5*1000 = 400}}}ml
The second vessel would have milk = {{{3/(3+7)*1000 = 3/10*1000 = 300}}}ml
Thus total milk in mixture = 400+300 = 700ml
Total water in the mixture = 2*1000 - 700 = 1300ml
Ratio of Milk:Water = 700:1300 = 7:13

Q8. If A completes a work in 5 days and B completes the same work in 3 days, how long would it take to complete the work if both work together?
A8. Rate of completion of work = 1/(Number of days taken) per day
Rate at which A completes the work = 1/5 per day
Rate at which B completes the work = 1/3 per day
Rate at which both will completer the work together = {{{1/5+1/3 = (3+5)/15 = 8/15}}} per day.
Thus time taken to complete the work = 1/(8/15) = 15/8 days