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Initial Ratio (Alcohol : Water) = 11 : 6 (Total units = 17)

Final Ratio (Alcohol : Water) = 5 : 3

Equate Alcohol: multiply initial by 5 and final by 11 → New Ratios: 55 : 30 and 55 : 33.

Total initial 85 units = 85 litres ⇒ 1 unit = 1 litre.

Water added = 33 − 30 = 3 units = 3 litres.

∴ The correct answer is 3 litres.

Alternate Method

Given: Total volume = 85 litres, Initial ratio = 11 : 6, Final ratio = 5 : 3.

Formula: Value of one part = Total Volume ÷ Sum of ratio parts.

⇒ Initial Alcohol = (11/17) × 85 = 55 litres.

⇒ Initial Water = (6/17) × 85 = 30 litres.

⇒ Let x litres of water be added.

⇒ New Alcohol / New Water = 55 / (30 + x) = 5 / 3.

⇒ 165 = 5 × (30 + x)

⇒ 165 = 150 + 5x

⇒ 5x = 15 ⇒ x = 3 litres.

∴ The correct answer is 3 litres.

Additional Information

Constant Quantity Concept

When only one component (e.g., water) is added to a mixture, the quantity of the other component (e.g., alcohol) remains constant. Equating the constant part in both ratios simplifies calculations.

Alligation Method

Can be used by taking water concentration. Initial water (6/17) and added pure water (1/1) are mixed to get a final concentration of 3/8.

Replacement vs Addition

In addition, total volume increases. In replacement, a portion of the mixture is removed and the same volume of a component is added, keeping total volume constant.

Given:

A filled the tank = 8 hours 

Formula:

(A + B + C)’s 1 hour work = 1/A + 1/B + 1/C

Calculation:

Suppose pipe A alone takes x hours to fill the tank.

Then, pipes B will take x/2 and C will take x/6​ hours respectively to fill the tank.

⇒ 1/x ​+ 2/x ​+ 6/x ​= 1/8​

⇒ 9/x ​= 1/8​

⇒ x = 72 hrs.

B will take = 72/2 = 36 hours.

∴ Pipe B alone take 36 hours to fill the tank.

Given:

Perimeter of square field – Side of square = 48 cm

Side of square field B = Side of square field A – 4 cm

Formula used:

Area of square field = (side)²

Perimeter of square field = 4 × (side)

Calculation:

Perimeter of square field – Side of square = 48 cm

⇒ (4 × Side) – Side = 48

⇒ 3 × Side = 48

⇒ Side = 16 cm

⇒ Side of square field B = 16 cm – 4 cm

⇒ 12 cm

Area of square field B = (12)²

⇒ 144 cm²

Given:

Ratio of the first to second is 3 : 4

Ratio of second to the third is 8 : 5

Sum of three numbers is 190

Calculations:

Let the three numbers be A, B and C respectively

⇒ A : B = 3 : 4       …..(1)

⇒ B : C = 8 : 5       …..(2)

Multiplying (1) by 2, 

⇒ A : B = 6 : 8

⇒ B : C = 8 : 5

⇒ A : B : C = 6 : 8 : 5

Sum of ratio = 6 + 8 + 5 = 19

⇒ C = (5/19) × 190 = 50

∴ Third number is 50.

Shortcut Trick "1" becomes "2" in 4 years

 "2" becomes "4" in 8 years

"4" becomes "8" in 12 years

∴ Required Amount = 950 × 8 = Rs. 7600

TRADITIONAL METHOD

Given

Principal = Rs. 950 

Principal double itself in 4 years

Formula used

Amount = P{1 + (r/100)}n

where,

P = Principal

r = Rate

n = Time

Calculation

According to question,

Amount = P{1 + (r/100)}n

⇒ P{1 + (r/100)}4 = 2P

⇒ {1 + (r/100)}4 = 2      ----(i)

After 12 years the amount will be, Amount = P{1 + (r/100)}12

⇒ P[{1 + (r/100)}4]3

⇒ P(2)3

⇒ 8P

Amount after 12 years = 950 × 8 = Rs. 7600.

∴ The Amount after 12 years will be Rs. 7600

Hence, Amit is facing towards West when he is at point F (end point).

Hence the distance between starting point (A) and end point (F) is 5 m.

At point C, Amit is facing towards South direction.

Hence, point D is in the South-East direction with respect to point F.

Hence, the answer would be Y.