1). A dealer sell two A and B article at 20% and 30% profit. Total profit earned by him is 140 . Cost price of article A is 50 less than cost price if article B. Find the cp of B.
2). Vessel contain milk and water in 7:1. 1/10 mixture taken out and 3 litre water added. Finally jar milk and water ratio is 6:1. Find initial quantity of mixture.
3). A,B,C started a business at initial capital in ratio 2:3:4. At the end of six month, A invest amount such that his initial capital become equal to B’s initial investment. B’s annual profit is 3000. What is total profit?
4). Suman spend 36% on food. Remaining ¼ on brother and ⅜ on sister. Difference of amount given to brother and sister is 1200. What is suman total savings ?
5). Time taken by A alone to finish a work is 50% more than time taken by A+B together. B is thrice as efficient as C. if B+C together can complete work in 22.5 days, how many days taken by A alone to complete the work?
6).A vessel contains milk and water in the ratio of 7:1. 1/10th mixture is removed and 3 litres of water is added. The final ratio of milk and water is 6:1. Find the initial quantity of the mixture.
Detailed Solutions:
1). Cost price of B = x
Cost price of A = x - 50
= (x – 50) × 20/100 + x × 30/100 = 140
= (20x – 1000 + 30x)/100 = 140
= 50x – 1000 = 140 × 100
= 50x – 1000 = 14000
= 50x = 14000 + 1000
= 50x = 15000
= x = 15000/50
= x = 300
2) . Milk and Water = 7x : 1x
1/10 is take out = 7 – 0.7 : 1 – 0.10
Milk and Water = 6.3x : 0.9x
Add 3 litres of water and after add that ratio is 6 : 1
= 6.3x/0.9x + 3 = 6/1
= 6.3x = 6 × 0.9x + 3
= 6.3x = 5.4x + 18
= 6.3x – 5.4x = 18
= 0.9x = 18
X = 18/0.9
X = 20
Initial quantity of Milk and Water
= 7x : 1x
= 7 × 20 : 1 × 20
= 140 : 20
3). A : B : C = 2 : 3 : 4
= (2 × 6) + (3 × 6) : 3 × 12 : 4 × 12
= (12 + 18) : 36 : 48
= 30 : 36 : 48
= 5 : 6 : 8
B’s annual profit is 3000
= 3000/6 = 500
Total profit = 500 × 19
= 9500
4). Food = 36x
Brother = 16x
Sister = 24x
Difference of brother and sister
= 24x – 16x = 1200
= 8x = 1200
= x = 1200/8 = 150
X = 150
Savings = Income – Expenditure
= 100 – 36 – 16 -24 = 24
Savings is 24x = 24 × 150
= 3600
5). B and C working together = 22.5
B is thrice as efficient as C = 22.5 × 4/3 = 30
B finishes the work in 30 days
C finishes the work in 90 days
A and B together finish the work in x days
A alone to finish a work is 50% more than time taken by A+B together
So A = 1.5x
= 1/x – 1/30 = 1/1.5x
= 1/x – 1/1.5x = 1/30
= 1.5x - 1x/1.5x = 1/30
= 0.5x/1.5x = 1/30
= 1/30 × 1.5x/0.5x
X = 10
Therefore A = 1.5x
= A = 1.5 × 10 = 15
A can do it in 15 days
