4 RATIOS AND PROPORTIONS
What is a ratio?
A ratio is a representation of distribution ofa value present among the persons present and is shown
follows:
Ifa total is divided among A, B and C such that A got 4 parts, B got 5 parts andC got 6 parts then it
represented in ratio as A:B:C = 4:5:6.
So, 4:5:6 means that the total value is divided into 4+5+6= 15 equal parts and then distributed as per t
ratio.
Example1:
Divide Rs. 580 between A and B in the ratio of 14:15.
Soln: A:B =14:15 580is divided into 29 equalparts=>each part =Rs. 20.
So A's share = 14 parts = 14 x 20 Rs. 280
B's share = 15 parts =Rs. 300.
Example 2:
IfA:B-2:3 and B:C= 4:5 then find A:B:C.
Soln: To combine two ratios the proportions common for them shall be in
equal parts. Here the common proporto
is B for the given ratios.
Making B equal in both ratios they become 8:12 and 12:15=>A:B:C 8:12:15.
Example 3:
Three numbers are in the ratio of 3:4:8 and the sum ofthese numbers is 975. Find the three numbers.
Soln: Let the numbers be 3x, 4x and 8x. Then their sum =
3xt4x+8x =
15x= 975 = > = 65.
So the numbers are 3x = 195, 4x = 260 and 8x = 520.
Example 4:
Two numbers are in the ratiool4:5.I1 the diflerence between these numbers is 24, then tind
the numc
Saln et the numbers be 4x and Sx.
Their difference= 5x- 4xx24 (given)
So the numbers are 4x 96 and 5x 120,
Example 5:
, Civen two numbers are in the ratio of 3 :4. If8 is added to each of them, their ratio is
two numbers.
changed to 5:6. Find
Let the numbers be a and b.
Soln:
A:B 3:4=>A/B=3/4.
Also, (A+8) /(B+8) = 5/6.
Solving we get, A=12 and B =
16
Example 6:
Agarrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers
For how many more days will the provisions last?
will join the group.
Soln: Actually after 180 days,
If 120 members are there provisions come for 60 more days (since total 240 days)
But now 180 members are there.
So number of days =(120/180) X 60 =
40 days.
Example 5:
If24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs
a day do it?
Soln: 24 men- 12 hrs- 16 days
8 men-6 hrs ? days -
(n)
n=16 X(12/6) X(24/8) ( since no ofhrs reduced no of days has to increase and no of men reduced also
increases no of days i.e., inverse
proportional)
=>n= 96 days.
EXERCISE
. Divide Rs. 1870 into three parts in such a
way that halfofthe first part, one-third of the second part and one-
sixth of the third part are
equal.
. 241, 343, 245 2 400, 800, 670
3. 470, 640, 1160 4. None
2 Divide Rs. 500 amongA, B, C and D so thatA and B
together get thrice as much as C and D together, B gets
our times C gets and C gets 1.5 times as much as D. Now the amount C
of what gets
1. 300 75
3 125 4. None
What is a ratio?
A ratio is a representation of distribution ofa value present among the persons present and is shown
follows:
Ifa total is divided among A, B and C such that A got 4 parts, B got 5 parts andC got 6 parts then it
represented in ratio as A:B:C = 4:5:6.
So, 4:5:6 means that the total value is divided into 4+5+6= 15 equal parts and then distributed as per t
ratio.
Example1:
Divide Rs. 580 between A and B in the ratio of 14:15.
Soln: A:B =14:15 580is divided into 29 equalparts=>each part =Rs. 20.
So A's share = 14 parts = 14 x 20 Rs. 280
B's share = 15 parts =Rs. 300.
Example 2:
IfA:B-2:3 and B:C= 4:5 then find A:B:C.
Soln: To combine two ratios the proportions common for them shall be in
equal parts. Here the common proporto
is B for the given ratios.
Making B equal in both ratios they become 8:12 and 12:15=>A:B:C 8:12:15.
Example 3:
Three numbers are in the ratio of 3:4:8 and the sum ofthese numbers is 975. Find the three numbers.
Soln: Let the numbers be 3x, 4x and 8x. Then their sum =
3xt4x+8x =
15x= 975 = > = 65.
So the numbers are 3x = 195, 4x = 260 and 8x = 520.
Example 4:
Two numbers are in the ratiool4:5.I1 the diflerence between these numbers is 24, then tind
the numc
Saln et the numbers be 4x and Sx.
Their difference= 5x- 4xx24 (given)
So the numbers are 4x 96 and 5x 120,
Example 5:
, Civen two numbers are in the ratio of 3 :4. If8 is added to each of them, their ratio is
two numbers.
changed to 5:6. Find
Let the numbers be a and b.
Soln:
A:B 3:4=>A/B=3/4.
Also, (A+8) /(B+8) = 5/6.
Solving we get, A=12 and B =
16
Example 6:
Agarrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers
For how many more days will the provisions last?
will join the group.
Soln: Actually after 180 days,
If 120 members are there provisions come for 60 more days (since total 240 days)
But now 180 members are there.
So number of days =(120/180) X 60 =
40 days.
Example 5:
If24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs
a day do it?
Soln: 24 men- 12 hrs- 16 days
8 men-6 hrs ? days -
(n)
n=16 X(12/6) X(24/8) ( since no ofhrs reduced no of days has to increase and no of men reduced also
increases no of days i.e., inverse
proportional)
=>n= 96 days.
EXERCISE
. Divide Rs. 1870 into three parts in such a
way that halfofthe first part, one-third of the second part and one-
sixth of the third part are
equal.
. 241, 343, 245 2 400, 800, 670
3. 470, 640, 1160 4. None
2 Divide Rs. 500 amongA, B, C and D so thatA and B
together get thrice as much as C and D together, B gets
our times C gets and C gets 1.5 times as much as D. Now the amount C
of what gets
1. 300 75
3 125 4. None
