This document discusses ratio and proportion concepts including unitary systems and partnerships. It categorizes ratio and proportion into basics, mixtures, and allocation rule. It provides 3 examples of unitary system problems involving work, toys production, and wall construction. It also includes 1 partnership problem calculating individual shares of profits for partners A, B, and C based on their investment amounts and time involved in the business.

1. Ratio & Proportion - 4

2. Ratio and proportion is categorized into 3 types
 Basics
 Mixtures
 Allegation rule
 Unitary system
 Partnership

3. Unitary System

4. 1. A 20 men are taking 36 days to do a work how many days will 24
men take to do the same job?
2. 30 men can prepare 4000 toys in 45 days by working at a rate 6
hrs/day. How many toys approximately can 40 women can
prepare working are a rate of 8 rs/day ?
3. 120 men take 48 days to construct a wall of length 600m, breadth
18m, height 12m by working at a rate of 8hrs/day. How many
days will 160 men to construct a wall of length 900m, breadth
27m, and height 18m by working at a rate of 12hrs/day ? It is
given that men in the 2nd case are twice as efficient as men in the
1st case.

5. 1. A 20 men are taking 36 days to do a work how many days will 24
men take to do the same job?
Ans :
Total work done = Total men Total number of days
For 20 men and 36 days, The work done = 20 36 = 720
This work has to be done by 24 men.
Therefore total number of days = = 30 days
Number of days = 30

6. 30 men can prepare 4000 toys in 45 days by working at a rate 6
hrs/day. How many toys approximately can 40 men can prepare
working are a rate of 8 rs/day ?
2.
men hours toys days
30 6 4000 45 (1)
40 8 ? 45 (2)
 Total hours of work = 30 6 = 180 hrs /day -- for (1)
 Total hours of work = 40 8 = 320 hrs /day -- for (2)
40 men can prepare 7111 toys
Ans :
180 = 4000
320 = 7111
40 men can prepare 7111 toys at a rate of 8hrs/day.

8. 120 men take 48 days to construct a wall of length 600m, breadth
18m, height 12m by working at a rate of 8hrs/day. How many days
will 160 men to construct a wall of length 900m, breadth 27m, and
height 18m by working at a rate of 12hrs/day ? It is given that men in
the 2nd case are twice as efficient as men in the 1st case
3.
Men = 3 : 4
Length = 2 : 3
Breadth = 2 : 3
Height = 2 : 3
Effective = 1 : 2
Hours = 2 : 3
Ans :
Day = 48 : ?
 Days = 48
= days
Total work done = Total men Total number of days

9. Partnership

11. 1. A started a business with an investment of 6 lakhs. B joined with A after
3 months with an investment of 12 lakhs. But he left the business 3
months before the year end. C has replaced B with an investment of 24
lakhs . If by the year end, they have made profits to the extent of
1,80,000 then what is the share of B ?
Ans :
First we have to find out the percentages of all A , B, C
A has worked for 12 months
Total Value of A = Total money invested Total months
= 6 lakh 12 months = 72 lakhs
B has worked for 6 months and C worked for 3 months

12. Share of C = 60,000
Total Value of B = Total money invested Total months
= 12 lakh 6 months = 72 lakhs
Total Value of C = Total money invested Total months
= 24 lakh 3 months = 72 lakhs
Ratio of A : B : C = 72 : 72 : 72
= 1 : 1 : 1
Share of C = 1,80,000 = 60,000

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