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Given:

Speed of boat in still water = 5km/hr

Speed of current = 1km/hr

Total time taken = 1 hour

Assumption:

Let the distance be N km

Formula used:

⇒ Time taken to travel upstream = distance/speed = N/4

⇒ Time taken to travel downstream = distance/speed = N/6

Calculation:

⇒ Speed upstream = 5 – 1 = 4km/hr

⇒ Speed downstream = 5 + 1 = 6km/hr

According to question.

⇒ (N/6) + (N/4) = 1

⇒ 5N = 12

⇒ N = 2.4

∴ Distance is 2.4 km

GIVEN:

Initial solution = 18 l

Water evaporated = 6 l

Sugar % = 9%

CONCEPT:

When the solution is boiled only water evaporates and the amount of sugar remains the same.

CALCULATION:

Amount of sugar,

9% of 18 = 1.62 

After evaporation,

Remaining solution = 18 - 6 = 12 l

% of sugar in remaining solution,

⇒ 1.62/12 × 100

= 13.5%

Alternate Method 

Water in Initial Solution = (100 - 9)% of 18 = 91% of 18 = 16.38

Water Evaporated = 6 Litre

Remaining Water = 16.38 - 6 = 10.38

Remaining Solution = 18 - 6 = 12

Remaining Sugar = 12 - 10.38 = 1.62

Required% = (1.62/12) × 100 = 13.5%

Given:

C.I. = Rs 7280

P = Rs 10,000

T = 3 years

Formula used:

A = P × (1 + (r/n))^nt

Where, A = Amount, P = Principal amount, r = Rate of interest, n = number of times its getting compounded, t = time

Calculation:

A = 10,000 + 7280

⇒ A = 17280

⇒ 17280 = 10000 × (1 + (r/100)) ³

⇒ 1.728 = (1 + (r/100))³

⇒ 1.2 = (1 + (r/100))   (∵ Taking cube root)

⇒ r = 20%

∴ Rate of interest is 20%

Hint

1.2³ = 1.728

Find amount from interest given and solve the rest of question

Given:

Average of 5 number = 66.4

Average of the first 2 numbers = 67

Average of last 2 numbers = 75

Formula used:

Average = Sum of numbers/Number of units

Calculation:

Sum of all 5 numbers = 66.4 × 5 = 332

Sum of first 2 numbers = 2 × 67 = 134

Sum of last 2 numbers = 2 × 75 = 150

Middle number = 332 – (134 + 150)

⇒ 332 – 284

⇒ 48

∴ The middle number is 48

Given: 

Monthly expenditure of man on food = 40%

Monthly expenditure of man on entertainment = 20%

Monthly expenditure of man on house rent = 10%

Monthly expenditure of man on travel = 15%

Monthly savings = Rs. 3,000

Formula Used:

Income = Total Expenditures + Savings

Percentage = (Value/Total value) × 100

Calculation:

Monthly salary of man = 100%

Total monthly expenditures = 40% + 20% + 10% + 15% = 85%

Monthly saving = 100% – 85% = 15%

⇒ 15 = (3,000/Monthly income) × 100 

⇒ Monthly income = Rs. 20,000

∴ Monthly salary of man is Rs. 20,000.

Eight girls: Isha, Ishani, Ishita, Ishika, Ipshita, Ishu, Imma, and Ishprit.

1) Ishprit lives on the third floor.

2) Only three people live between Ipshita and Ishita.

3) Ishika lives immediately above Ipshita, but not on the top floor.

4) Ishani lives on an even floor below Ishu.

5) Only two girls live between Imma and Ishu, where Imma lives above.

Case III eliminate here as the condition of Imma and Ishu is not possible.

6) Isha does not live on any of the even-numbered floors.

Case II eliminates here as Isha will not live on any even-numbered floors.

The final arrangement is:

Hence, No one lives on the third floor below Ishprit.

Eight girls: Isha, Ishani, Ishita, Ishika, Ipshita, Ishu, Imma, and Ishprit.

1) Ishprit lives on the third floor.

2) Only three people live between Ipshita and Ishita.

3) Ishika lives immediately above Ipshita, but not on the top floor.

4) Ishani lives on an even floor below Ishu.

5) Only two girls live between Imma and Ishu, where Imma lives above.

Case III eliminate here as the condition of Imma and Ishu is not possible.

6) Isha does not live on any of the even-numbered floors.

Case II eliminates here as Isha will not live on any even-numbered floors.

The final arrangement is:

Hence, Ishprit lives immediately above Ishita.

Eight girls: Isha, Ishani, Ishita, Ishika, Ipshita, Ishu, Imma, and Ishprit.

1) Ishprit lives on the third floor.

2) Only three people live between Ipshita and Ishita.

3) Ishika lives immediately above Ipshita, but not on the top floor.

4) Ishani lives on an even floor below Ishu.

5) Only two girls live between Imma and Ishu, where Imma lives above.

Case III eliminate here as the condition of Imma and Ishu is not possible.

6) Isha does not live on any of the even-numbered floors.

Case II eliminates here as Isha will not live on any even-numbered floors.

The final arrangement is:

Hence, Ishani lives below Ishu.

Eight girls: Isha, Ishani, Ishita, Ishika, Ipshita, Ishu, Imma, and Ishprit.

1) Ishprit lives on the third floor.

2) Only three people live between Ipshita and Ishita.

3) Ishika lives immediately above Ipshita, but not on the top floor.

4) Ishani lives on an even floor below Ishu.

5) Only two girls live between Imma and Ishu, where Imma lives above.

Case III eliminate here as the condition of Imma and Ishu is not possible.

6) Isha does not live on any of the even-numbered floors.

Case II eliminates here as Isha will not live on any even-numbered floors.

The final arrangement is:

Hence, Isha lives on the 8^th floor is not true.

Eight girls: Isha, Ishani, Ishita, Ishika, Ipshita, Ishu, Imma, and Ishprit.

1) Ishprit lives on the third floor.

2) Only three people live between Ipshita and Ishita.

3) Ishika lives immediately above Ipshita, but not on the top floor.

4) Ishani lives on an even floor below Ishu.

5) Only two girls live between Imma and Ishu, where Imma lives above.

Case III eliminate here as the condition of Imma and Ishu is not possible.

6) Isha does not live on any of the even-numbered floors.

Case II eliminates here as Isha will not live on any even-numbered floors.

The final arrangement is:

Hence, Ishika lives on the floor just below the topmost most floor.