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Family Chart:

Given: 

“He is the son of my mother's only son.”

Means: Your mother’s only son = your brother

So, Brother’s son = Nephew.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: All numbers are factorials (!)

These numbers look like factorials:

2 = 2!

6 = 3!

24 = 4!

120 = 5!

720 = 6! 

So, Next should be: 7! = 5040

thus, Instead of 5040, the series has 1000, which is not a factorial number.

Hence, the correct option is "Option 3".

The logic followed here is:

Logic: In the first three sets, each number is double the previous number.

Given,

(11, 22, 44), (13, 26, 52), (15, 30, 60), (14, 28, 43)

Now, checking the options:

Option 1) (11,22,44)

⇒ 11 × 2 = 22

22 × 2 = 44

Option 2) (13,26,52)

⇒ 13 × 2 = 26

26 × 2 = 52

Option 3) (15,30,60)

⇒ 15 × 2 = 30

30 × 2 = 60

Option 4) (14,28,43)

⇒14 × 2 = 28

28 × 2 = 56 (but given 43)

 Hence, the correct option is "Option 4".

The logic followed here is:

Logic: the pattern is a @ b = a² + b

Given:

WRITE is coded as YTKVG,

Similarly,  READ = ?

Hence, the correct answer is "Option 1."

The logic followed here is:

Logic: (1^st number × 2^nd number) + (2^nd number +1) = 3^rd number.

Given:

If 5 # 3 = 19,

⇒ 5 # 3 = (5 × 3) + (3 + 1) = 15 + 4 = 19 

and 7 # 2 = 17,

⇒ 7 # 2 = (7 × 2) + (2 + 1) = 14 + 3 = 17

Similarly, 9 # 1?

⇒ 9 # 1 = 9 × 1 + (1 + 1) = 9 + 2 = 11

Hence, the correct answer is "Option 4."

Shortcut Trick

Initial Ratio (Milk : Water) = 7 : 3 (Total = 10 units)

Final Ratio = 1 : 1 → Equate Milk (since only water is added) → 7 : 7

Increase in Water units = 7 − 3 = 4 units

Given 10 units = 60 L ⇒ 1 unit = 6 L

Added Water = 4 units × 6 L = 24 L

∴ The correct answer is 24 L.

Alternate Method

Given: Total mixture = 60 L, Initial ratio (M:W) = 7 : 3, Final ratio (M:W) = 1 : 1.

⇒ Total parts in initial mixture = 7 + 3 = 10 units

⇒ Quantity of Milk = (7 ÷ 10) × 60 = 42 L

⇒ Quantity of Water = (3 ÷ 10) × 60 = 18 L

⇒ In the final 1 : 1 mixture, let the water added be x liters.

⇒ New Water content = 18 + x

⇒ Milk : Water = 42 : (18 + x) = 1 : 1

⇒ 42 = 18 + x

⇒ x = 42 − 18 = 24 L

∴ The correct answer is 24 L.

Additional Information

Constant Quantity Concept

When one component of a mixture is added or removed, the quantity of the other component remains constant. Always equate the parts of the constant component in the ratio calculations.

Ratio Balancing

To simplify calculations, multiply the final ratio by a factor that makes the non-changing substance equal in both ratios (e.g., if milk is 7 parts initially, make it 7 parts in the final ratio).

Percentage Method

Initial Milk % = 70%. In 1:1 ratio, Milk % = 50%. Using inverse variation: Total Volume₁ × %₁ = Total Volume₂ × %₂ ⇒ 60 × 70 = V_new × 50 ⇒ V_new = 84 L.

Family Chart:

Given: 

“She is the daughter of the only child of my grandmother.”

Aryan’s grandmother has only one child.

That child must be Aryan’s parent (either father or mother).

Therefore, the girl is Aryan’s Sister.

Hence, the correct answer is "Option 3".

Family Chart:

Given: 

My father’s wife → This is Ramesh’s mother. 

The two sons of my father’s wife → This means Ramesh and his brother, because both are sons of the same mother

The boy is the younger of the two sons → So the boy must be Ramesh’s younger brother. 

So, the football-playing boy is Ramesh’s brother.

Hence, the correct answer is "Option 1".

Given:

A = 11 / 19

B = 2 / 9

We need to find: A − B

Formula Used: a/b − c/d = (ad − bc) / bd

Calculation:

A − B = (11/19) − (2/9)

Take LCM of 19 and 9:

19 × 9 = 171

Now convert into like fractions:

(11 × 9 − 2 × 19) / 171

= (99 − 38) / 171

= 61 / 171

Now convert to decimal:

61 ÷ 171 ≈ 0.356 ≈ 0.36

∴ The correct answer is "Option 1."

Shortcut Trick

Step 1: Calculate the sum of the given numbers: 35 + 46 = 81.

Step 2: Multiply the result by 2 as per the requirement: 81 × 2 = 162.

∴ The correct answer is 162.

Alternate Method

Given:

First number = 35

Second number = 46

Multiplier = 2

Calculation:

According to the question, we need to find the result of [(35 + 46) × 2].

⇒ Result = (35 + 46) × 2

⇒ Result = 81 × 2

⇒ Result = 162

Alternatively, using the distributive property:

⇒ (35 × 2) + (46 × 2)

⇒ 70 + 92 = 162

∴ The correct answer is 162.

Additional Information

BODMAS Rule

This rule dictates the order of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction. In this problem, the sum (addition) is performed first because it is implied by the phrasing before the multiplication.

Distributive Property

The property states that a × (b + c) = (a × b) + (a × c). This allows for multiplying each term inside the sum individually before adding them together.