Search Previous Year Questions

Shortcut Trick

Difference in percentage votes = 52% − (100% − 52%) = 52% − 48% = 4%.

Since 4% of valid votes = 98 votes, then 100% of valid votes = (98 ÷ 4) × 100 = 2450.

Total votes polled = Valid votes + Invalid votes = 2450 + 68 = 2518.

∴ The correct answer is 2518 votes.

Alternate Method

Given: Invalid votes = 68, Winner share = 52%, Victory margin = 98 votes.

Let the total valid votes be V.

⇒ Winner = 52% of V

⇒ Loser = (100 − 52)% of V = 48% of V

⇒ Margin = 52% of V − 48% of V = 4% of V

⇒ 4% of V = 98

⇒ V = (98 × 100) ÷ 4 = 2450

⇒ Total votes polled = V + 68 = 2450 + 68 = 2518

∴ The correct answer is 2518 votes.

Additional Information

Percentage Change Base

Always ensure the percentage is calculated on the Valid Votes base unless the question specifies it is on the Total Polled Votes.

Successive Elections

If voters didn't cast votes, subtract them from Total Voters before calculating Invalid Votes: Total → Cast → Valid → Result.

Shortcut Trick

Market Price (MP) represents 100%.

Discount = 12% ⇒ Selling Price (SP) = 100% − 12% = 88%.

Given SP = Rs. 22,880.

Using unitary method: 88% = 22,880.

1% = 22,880 ÷ 88 = 260.

100% = 260 × 100 = 26,000.

∴ The correct answer is Rs. 26,000.

Alternate Method

Given → Selling Price (SP) = Rs. 22,880 | Discount Percentage = 12% Formulas: SP = MP × (100 − Discount%) ÷ 100 | MP = (SP × 100) ÷ (100 − Discount%)

⇒ Let the Market Price (MP) be x. ⇒ SP = MP − Discount ⇒ 22,880 = x − (12% of x) ⇒ 22,880 = x − 0.12x ⇒ 22,880 = 0.88x ⇒ x = 22,880 ÷ 0.88 ⇒ x = 26,000

∴ The correct answer is Rs. 26,000.

Additional Information

Market Price & Discount

Market Price (List Price) is the price printed on the product. Discount is always calculated on the Market Price.

Ratio Method

12% discount = 12/100 = 3/25. If MP = 25 units, Discount = 3 units, then SP = 22 units. 22 units = 22,880 ⇒ 1 unit = 1,040 ⇒ 25 units = 26,000.

Shortcut Trick

Ratio of investments P : Q : R = 35000 : 65000 : 75000 = 7 : 13 : 15.

Total ratio parts = 7 + 13 + 15 = 35 units.

Total loss =  ₹ 70000.

Value of 1 unit = 70000 ÷ 35 =  ₹ 2000.

Loss share of P = 7 units × 2000 =  ₹ 14000.

∴ The correct answer is  ₹ 14000.

Alternate Method

Given: Capital of P =  ₹ 35000, Q =  ₹ 65000, R =  ₹ 75000. Total loss =  ₹ 70000. Time = 2 years (constant).

Formula: Profit/Loss Share = Investment × Time Period.

⇒ Since time is the same for all, the loss is divided in the ratio of their capitals.

⇒ Ratio of loss = 35000 : 65000 : 75000 = 7 : 13 : 15.

⇒ Loss of P = [7 ÷ (7 + 13 + 15)] × 70000.

⇒ Loss of P = (7 ÷ 35) × 70000.

⇒ Loss of P = 7 × 2000 = 14000.

∴ The correct answer is  ₹ 14000.

Additional Information

Partnership Ratios

When the time period for all investments is the same, the profit or loss is shared strictly in the ratio of the capital invested.

Variable Time Investment

If partners invest for different durations, the ratio is calculated as: (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃).

Profit ratio is proportional to investment × time:

[A × 12] / [B × n] = 15/14

[10000 × 12] / [14000 × n] = 15/ 14

[120000 × 14 = 15 × 14000 × n]

n = 8 months

Common calculation

Profit ratio is proportional to investment × time:

[A × 12] / [B × n] = 15/14

[10000 × 12] / [14000 × n] = 15/ 14

[120000 × 14 = 15 × 14000 × n]

n = 8 months

Now, New case A invest for n = 8 months and B for 12 months

A invests = 10,000 for 8 months → A × time = 10,000 × 8 = 80,000

B invests = 14,000 for 12 months → B × time = 14,000 × 12 = 168,000

Profit ratio A : B = 80,000 : 168,000 = 10 : 21

Total ratio sum = 10 + 21 = 31

Total profit = 7750

B’s share z = [21/31] × 7750 = 5250

Here, boxes are F, G, H, I, J, K, L and M.

1. Box J is placed three boxes above the box M.

2. Two boxes placed between Box M and Box H.

3. Box G is placed just below the box J.

4. Two boxes are placed between Box L and Box K.

5. More than two boxes are placed between Box G and Box L.

6. Box I is placed above the box F but below the box K. Therefore, case 1 and case 2(b) are eliminated. Hence, the final arrangement is as follows

Hence, Box G is placed just above the Box K.

Here, boxes are F, G, H, I, J, K, L and M.

1. Box J is placed three boxes above the box M.

2. Two boxes placed between Box M and Box H.

3. Box G is placed just below the box J.

4. Two boxes are placed between Box L and Box K.

5. More than two boxes are placed between Box G and Box L.

6. Box I is placed above the box F but below the box K. Therefore, case 1 and case 2(b) are eliminated. Hence, the final arrangement is as follows

Since, only one box is placed above the box G and one box is placed below the box H.

Hence, the correct answer is Box H.

Here, boxes are F, G, H, I, J, K, L and M.

1. Box J is placed three boxes above the box M.

2. Two boxes placed between Box M and Box H.

3. Box G is placed just below the box J.

4. Two boxes are placed between Box L and Box K.

5. More than two boxes are placed between Box G and Box L.

6. Box I is placed above the box F but below the box K. Therefore, case 1 and case 2(b) are eliminated. Hence, the final arrangement is as follows

Since, only one box is placed between Box M and Box L and same number of box is placed between the Box F and Box L.

Hence, the correct answer is As many boxes placed between Box F and Box L.

Here, boxes are F, G, H, I, J, K, L and M.

1. Box J is placed three boxes above the box M.

2. Two boxes placed between Box M and Box H.

3. Box G is placed just below the box J.

4. Two boxes are placed between Box L and Box K.

5. More than two boxes are placed between Box G and Box L.

6. Box I is placed above the box F but below the box K. Therefore, case 1 and case 2(b) are eliminated. Hence, the final arrangement is as follows

Since, four boxes are placed below the Box M not two boxes. Therefore, statement first is incorrect.

No box is placed between Box I and Box M. Therefore, statement second is incorrect.

Four boxes placed below the box M and three boxes are placed above it.  Therefore, statement third is correct.

Only one box is placed between Box M and Box L. Therefore, statement fourth is incorrect.

Hence, the correct statement is The number of boxes placed below the box M is more than that of above it.

Here, boxes are F, G, H, I, J, K, L and M.

1. Box J is placed three boxes above the box M.

2. Two boxes placed between Box M and Box H.

3. Box G is placed just below the box J.

4. Two boxes are placed between Box L and Box K.

5. More than two boxes are placed between Box G and Box L.

6. Box I is placed above the box F but below the box K. Therefore, case 1 and case 2(b) are eliminated. Hence, the final arrangement is as follows

Since, Box L is placed two boxes above the Box F. Therefore, statement A is correct.

Box I is placed just below the Box M. Therefore, statement B is correct.

Three boxes are placed between Box H and Box K. Therefore, statement C is correct.

Hence, the correct answer is All of these.