Search Previous Year Questions

Calculations:

Total Number of books issued to A = 18 + 30 + 24 = 72

Total Number of fiction books issued to A = 72 × (25 /100)

Total Number of fiction books issued to A = 18

Calculations:

Total number of book issue in library P to all three people together = [18 + 20 + 25] = 63

Total number of book issue in library Q to all three people together = [30 + 35 +10] = 75

So, Total number of book issue in library P to all three people together is 75 – 63 = 12 less than the number of book issue in library Q to all three people together.

Shortcut Trick

Assume Total Population = 100 units.

Literates = 80 units, Illiterates = 20 units (Ratio 4 : 1).

Literate Females = 30% of 80 = 24 units | Illiterate Females = 20% of 20 = 4 units.

Total Females = 24 + 4 = 28 units → 56 (Given).

1 unit = 2 | Total population = 100 × 2 = 200.

∴ The correct answer is 200.

Alternate Method

Given: Ratio of Literate to Illiterate = 4 : 1. Total Females = 56.

Let Literate = 400x and Illiterate = 100x. Total Population = 500x.

⇒ Literate Females = 30% of 400x = 0.30 × 400x = 120x.

⇒ Illiterate Females = 20% of 100x = 0.20 × 100x = 20x.

⇒ Total Females = 120x + 20x = 140x.

⇒ 140x = 56

⇒ x = 56 ÷ 140 = 0.4

⇒ Total Population = 500 × 0.4 = 200.

∴ The correct answer is 200.

Additional Information

Ratio Distribution

To divide a quantity N in ratio a : b, the parts are [a/(a+b)] × N and [b/(a+b)] × N.

Percentage of a Group

If x% are males, then (100 − x)% are females, provided there are only two categories.

Unitary Method

Finding the value of a single unit (140 units = 56 → 1 unit = 0.4) to calculate the total required value.

Shortcut Trick

Circumference of Circle = π × d = (22/7) × 56 = 176 cm.

Perimeter of Rectangle = 2 × (L + B). Given L + B = diameter = 56 cm.

⇒ Perimeter = 2 × 56 = 112 cm.

Ratio = 176 : 112 = 11 : 7 (dividing both by 16).

∴ The correct answer is 11 : 7.

Alternate Method

Given:

Diameter (d) of circle = 56 cm.

Sum of length (L) and breadth (B) of rectangle (L + B) = 56 cm.

Formula Used:

⇒ Circumference of circle (C) = π × d

⇒ Perimeter of rectangle (P) = 2 × (L + B)

Calculations:

⇒ C = (22/7) × 56

⇒ C = 22 × 8 = 176 cm

⇒ P = 2 × 56 = 112 cm

⇒ Ratio = C / P = 176 / 112

⇒ Ratio = (16 × 11) / (16 × 7) = 11 / 7

∴ The correct answer is 11 : 7.

Additional Information

Circle Properties

Area of circle = πr² or (πd²)/4. Circumference = 2πr or πd.

Rectangle Mensuration

Area of rectangle = L × B. Diagonal = √(L² + B²).

Standard π Values

For calculations involving 7 or its multiples, use π ≈ 22/7 for easier cancellation.

Shortcut Trick

When distance is constant, time is inversely proportional to speed (T ∝ 1/S).

Initial speed = 100% → New speed = 100% + 100% = 200%.

Speed ratio = 1 : 2 ∴ Time ratio = 2 : 1.

2 units = 10 hours ⇒ 1 unit = 5 hours.

∴ The correct answer is 5 hr.

Alternate Method

Given: Initial Speed (S₁) = 25 km/h, Initial Time (T₁) = 10 hours.

Formula Used: Distance = Speed × Time

⇒ Total Distance = S₁ × T₁ = 25 × 10 = 250 km.

⇒ New Speed (S₂) = 25 + (100% of 25) = 25 + 25 = 50 km/h.

⇒ New Time (T₂) = Distance ÷ S₂

⇒ T₂ = 250 ÷ 50 = 5 hours.

∴ The correct answer is 5 hr.

Additional Information

Inverse Proportion Rule

If distance is constant, S₁ × T₁ = S₂ × T₂. This allows for quick calculation without finding the actual distance.

Percentage Increase in Speed

A 100% increase means the value doubles (New = Old × 2). Similarly, a 200% increase means the value triples.

Average Speed

For two equal distances covered at speeds x and y, Average Speed = (2 × x × y) ÷ (x + y).

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

 

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

 

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

 

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

 

R is the Sectional Officer.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

 

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

 

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

 

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

Three designations are there between W and T.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

 

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

 

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

 

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

W is just junior to Deputy General Manager.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

 

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

 

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

 

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

Q is the Manager.

From the given instructions:

Eight people P, Q, R, S, T, U, V and W, they have different designation as General Manager, Deputy General Manager, Assistant General Manager, Manager, Assistant Manager, Sectional Officer, Cashier and Clerk. The order of seniority is same as given above i.e. General manager is the senior-most and the Clerk is the junior-most. So, we can a draw a structure as:

 

1. Only five people have their designations between S and V. Sectional Officer is senior to V. So, we have two cases:

 

2. More than two people are senior to Q. Q is immediately junior to W. U is senior to at least three designations. U is junior to W. Only three people have their designation between P and U.

So, from above conditions we can say that U can only be placed at Assistant Manager. So, we can say,

 

So, here we can clearly see that Case 1 is invalid, as there is no space to place P. So, Case 1 gets cancelled out.

3. S is senior to R, who is senior to T.

So, Final Arrangement:

No designations is there below V. V is having junior most designation.