TS Police SI Mains 2018 Arithmetic and Reasoning

Let total work be 280 units. Hence, P completes 7 units/day and Q completes 8 units/day 
Total work done per day working together = 15 units
Total work done in 14 days together = 15*14 = 210 units 

Remianing work = 70 units 
Time taken by Q to complete work = 70/8 days 

Let the capacity of each man and woman be m and w units/day respectively

320 m*d = 360 w*d 
m = (9/8)*w

All men and women work together , then work done in a day = 20m + 20w = 20 * (17/8) * w = 42.5*w
Total days needed to complete work = 360 w*d/42.5*w = 8.47 days

Total hours required by A = 120 hours 
Total hours required by B = 140 hours 

Total hours needed by both working together = (120*140)/260 = 840/13 hours
But, A and B work 7 hours each day 

Hence, total days required together = 840/(13*7) = 120/13 days 

Let the total work be 120 units 
Hence, A works a = 5 units/day and B works b = 4 units/day 

B completes remaining work in 12 days. Hence, B completes 48 units alone.
This means A and B together completed = 120 - 48 = 72 units 
Total days A and B worked together = 72/(5+4) = 8 days 

Effective selling price = 0.95 x MP = 0.95 x 1.25 x CP = 1.1875 CP 

$$\therefore\ $$Profit percentage = $$\frac{1.1875CP-CP}{CP}\times100$$ = 18.75% = $$18\frac{3}{4}$$%

Hence, the correct answer is Option A

Let the cost price be CP 

2500 - CP = 7*(CP - 2100) 
8*CP = 17200
CP = 2150 

Now, to earn 20% profit = 1.2*2150 = 2580 

Let the price at which item is originally sold = S 

Given that 0.8*S = 0.92*CP (CP is cost price) 
S = 1.15*CP 

This means profit earned by selling at S is 15% over CP

Profit percentage of A = $$\frac{100}{350}\times100$$ = $$\frac{2}{7}\times100$$% 

Profit percentage of B = $$\frac{120}{540}\times100$$ = $$\frac{2}{9}\times100$$%

Difference = $$\frac{2}{7}\times100-\frac{2}{9}\times100$$ = $$\frac{400}{63}$$

Hence, the correct answer is Option A

Given, Total time = 56 min = $$\frac{56}{60}$$ hr

According to the problem,

$$\frac{\frac{2}{3}x}{4}+\frac{\frac{x}{3}}{5}=\frac{56}{60}$$

$$\frac{2x}{4}+\frac{x}{5}=\frac{56}{20}$$

$$\frac{10x+4x}{20}=\frac{56}{20}$$

$$14x=56$$

$$x=4$$ km

Hence, the correct answer is Option C

Assume Jan 1, 2000 was a Sunday. Also, 2000 was a leap year. 
So a leap year which starts on a Sunday would have the same calendar as 2000. 
2004 starts on a Friday. 2008 starts on a Wednesday. Following the same pattern, we can see that 2028 begins on Sunday. 
Hence, the answer.