Total capacity of Cistern = LCM of 16, 20 and 40 = 80 units

Efficiency of A = 80/16 = 5 units/min

Efficiency of B = 80/20 = 4 units/min

Efficiency of C = - 60/40 = - 2 units/min

Efficiency of A, B and C together = 5 + 4 - 2 unit/min = 7 units/min

Concept:

distance travel by a train with speed s for time t is d = s × t

Explanation:

Let d be the distance, s be the speed and t be the time

If the speed of a train is increased by 20%, its travel time between two stations reduces by 2 hrs.

12(t - 2) = 8(t + 3)

3(t - 2) = 2(t + 3)

3t - 6 = 2t + 6

t = 12

the normal duration of travel = 12 hr

Option (2) is correct.

Ratio in which the profit will be shared = Investment × Time for which investment was made

⇒ (1 × 12) : (2 × 11) : (3 × 10) : (4 × 9) : (5 × 8) : (6 × 7) : (7 × 6) : (8 × 5) : (9 × 4) : (10 × 3) : (11 × 2) : (12 × 1)

⇒ 12 : 22 : 30 : 36 : 40 : 42 : 42 : 40 : 36 : 30 : 22 : 12

Here we can see that shares of both F and G in the profit will be maximum.

Concept Used:

SP = CP + Profit

Profit% = (Profit/CP) × 100

CP = Cost Price, SP = Selling Price

Calculation:

A person bought an article and sold it at a profit of 20%:

Let's consider CP₁ is 100.

⇒ SP = 100 + 100 × (20/100) = 120

Had he bought it at 20% less:

⇒ CP₂ = 100 - 100 × (20/100) = 80

Since he still sells it at the same selling price of 120,

⇒ Profit = 120 - 80 = 40

⇒ Profit% = (40/80) × 100 = 50%

∴ The Profit Percentage is 50%.

Shortcut Trick

⇒ SP / CP = (100 + 20) / (100 - 20)

⇒  SP / CP = 120 / 80

⇒ Profit% = [(120 - 80) × 100] / 80 

⇒ 400 / 80 = 50% 

∴ The profit percentage is 50%.

The logic followed is:

Thus the total number of deaths due to dengue in village 'Z' in the years 2014 and 2015 are:

15 + 10

= 25

Hence, the correct answer is "25".

Given:

time taken by intercity train =  45 minutes

Concept Used:

speed is inversely proportional to time when distance is same

Calculation:

⇒ Ratio of time taken = 45 : 48 = 15 : 16

⇒ Ratio of speed = 16 : 15

⇒ 1 units ratio = 5 km/hrs.

⇒ 16 units ratio = 80 km/hrs.

∴ Distance = 80 × 45/60 = 60 km

Given:

Spent on food = 25%

Spent on house rent = 30%

Spent on travel = 11%

Spent on Education = 19%

Calculation:

Let the total income be Rs. X.

Total expenditure = X × (25% + 30% + 11% + 19%)

⇒ (X × 85%)

Total Saving = [X - (X × 85%)]

⇒ (X × 15%)

According to question,

(X × 15%) = Rs. 8760

⇒ X = Rs. [(8760 × 100)/15]

⇒ Rs. (584 × 100)

⇒ Rs. 58400

So, Expenditure on travel = 11% of Rs. 58400

⇒ (11/100) × Rs. 58400

⇒ Rs. 6424

∴ The amount spent on travel is Rs. 6424.

Alternate Method

Total Income = 100%

Total expenditure = (25% + 30% + 11% + 19%)

Savings = [100% - (25% + 30% + 11% + 19%)]

⇒ 15%

Expenditure on Travel = Rs. [(8760/15) × 11]

⇒ Rs. 6424.

∴ The amount spent on travel is Rs. 6424.

Given:

P = 10000

R = 20%

T = 2 years

Formula used:

Where,

A = Amount

CI = Compound interest

SI = Simple interest

P = Principal amount

R = Rate of interest

T = Time period

Calculations:

Joe’s interest = SI = (10000 × 20 × 2)/100

⇒ 1000 × 4

⇒ Rs.4000

Ben’s interest = CI = 10000 × [1 + (20/100)]² – 10000

⇒ 10000 × [(6/5)² – 1]

⇒ 10000 × (36 - 25)/25

⇒ 400 × 11

⇒ Rs.4400

⇒ Difference in interests = Rs. 4400 – Rs. 4000 = Rs. 400

∴ The difference between the interests earned by Ben and Joe is Rs.400

Alternate Method

Convert percentage into fraction

20% = 1/5

⇒ SI = 2000 + 2000 = 4000

⇒ CI = 2000 + 2000 + 400 = 4400

⇒ CI – SI = 400

∴ Difference between the interests is Rs.400

For compound interest:

Where,

A = Amount

P = Principal

R = rate %

t = time in years

Given, A sum of Rs. 12,000 deposited at compound interest becomes double after 5 years.

P = 12000

A = 2 × P = 24000

t = 5 years

R = ?

Substituting from eq 1 we have

⇒ A = 12000 × 2⁴

⇒ A = 12000 × 16

⇒ A = Rs. 192000

Given:

The number of employees working in five sectors and the respective ratio of males and females are given.

Calculations:

Number of employees in P sector = 650

The number of male employees and female employees in P sector be 6x and 7x

Total employees = (6x + 7x) = 13x

Number of male employees in P sector = 650 × 

⇒ 6 × 50 = 300

Number of employees in R sector = 850

The number of male employees and female employees in R sector be 9x and 8x

Total employees = (9x + 8x) = 17x

Number of female employees in R sector = 850 × 

⇒ 8 × 50 = 400

Required total male employees from P sector and female employees from R sector

⇒ (300 + 400) = 700

∴ The answer is 700.