Search Previous Year Questions

Given:

328 ÷ 8 + 25 × 2.4 + ? = (11)2

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

328 ÷ 8 + 25 × 2.4 + ? = (11)²

⇒ 41 + 60 + ? = 121

⇒ 101 + ? = 121

⇒ ? = 20

∴ 20 should come in place of the question mark (?).

Given:

15 × 678 - 10 × 802 + 60 ÷ 6 = ? × 50 ÷ 5

Concept Used:

Calculation:

15 × 678 - 10 × 802 + 60 ÷ 6 = ? × 50 ÷ 5

⇒ 10170 - 8020 + 10 = ? × 10

⇒ 2160 = ? × 10

⇒ 2160/10 = ?

⇒ ? = 216

∴ The value of ? is 216

Calculation:

We use the BODMAS rule as follows:

According to the rule ‘division’ should be solved first

⇒ 549 ÷ 3 × 54 - 25 × 321 + 31 = ?

⇒ 183 × 54 - 25 × 321 + 31 = ?

⇒ 9882 - 8025 + 31 = ?

⇒ 9913 - 8025 = ?

⇒ ? = 1888

∴ required answer is 1888.

Shortcut Trick

Ratio of Boat Speed (u) : Stream Speed (v) = 16 : 5

Upstream Speed (u−v) = 11 units | Downstream Speed (u+v) = 21 units

Upstream Speed = 33 km ÷ 1.5 hours = 22 kmph ⇒ 1 unit = 2 kmph

Downstream Speed = 21 × 2 = 42 kmph

Time Downstream = (35 ÷ 42) × 60 = 50 min

∴ The correct answer is 50 min.

Alternate Method

Given: Ratio of stream speed (v) to boat speed (u) = 5 : 16. Upstream distance = 33 km, Upstream time = 90 min (1.5 hours).

Formula Used: Speed = Distance ÷ Time; Upstream Speed (S_up) = u − v; Downstream Speed (S_down) = u + v.

⇒ Let Boat speed = 16x and Stream speed = 5x

⇒ Upstream speed = 16x − 5x = 11x

⇒ 11x = 33 km ÷ 1.5 hr = 22 kmph

⇒ x = 2 kmph

⇒ Downstream speed = 16x + 5x = 21x = 21 × 2 = 42 kmph

⇒ Time taken for 35 km downstream = (35 ÷ 42) hours

⇒ Time in minutes = (35 ÷ 42) × 60 = 5 × 10 = 50 min

∴ The correct answer is 50 min.

Additional Information

Relative Speed in Water

Downstream speed is the sum (u + v) and Upstream speed is the difference (u − v) of boat and stream speeds.

Boat Speed Calculation

Speed of boat in still water (u) = (Downstream Speed + Upstream Speed) ÷ 2.

Stream Speed Calculation

Speed of stream (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Shortcut Trick

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

Ratio of Capitals = 32000 : 20000 = 8 : 5.

Time for Vaibhav = x, Time for Ashish = (x − 6).

Ratio = (8 × x) : (5 × (x − 6)) = 12 : 5.

Solving 8x ÷ (5x − 30) = 12 ÷ 5 ⇒ 40x = 60x − 360 ⇒ 20x = 360 ⇒ x = 18.

∴ The correct answer is 18 months.

Alternate Method

Given: Vaibhav Investment = Rs. 32000, Ashish Investment = Rs. 20000, Profit Ratio = 12 : 5, Ashish joined after 6 months.

Formula: Profit = Investment × Time period

⇒ Let Vaibhav invested for x months.

⇒ Ashish joined 6 months later, so his time = (x − 6) months.

⇒ (32000 × x) ÷ (20000 × (x − 6)) = 12 ÷ 5

⇒ (32 × x) ÷ (20 × (x − 6)) = 12 ÷ 5

⇒ (8x) ÷ (5 × (x − 6)) = 12 ÷ 5

⇒ 8x ÷ (x − 6) = 12

⇒ 8x = 12x − 72

⇒ 4x = 72 ⇒ x = 18 months.

∴ The correct answer is 18 months.

Additional Information

Partnership Principle

In a partnership, the profit is distributed among partners in the ratio of the product of their investment and time duration.

Time Calculation

If a person joins 'n' months after the start, their investment duration is (Total Time − n).

Shortcut Trick

Assume Marked Price (MP) is 100.

Given Discount = 20%, so Selling Price (SP) = 100 − 20 = 80.

Difference (MP − CP) = 50% of SP = 0.5 × 80 = 40.

Since MP − CP = 40, then 100 − CP = 40 ⇒ Cost Price (CP) = 60.

Ratio MP : CP = 100 : 60 = 5 : 3.

∴ The correct answer is 5 : 3.

Alternate Method

Given: MP − CP = 0.5 × SP and Discount% = 20%

Formulas: SP = MP × (100 − D%) ÷ 100

⇒ Let Marked Price be M and Cost Price be C.

⇒ Selling Price (S) = M − 0.20M = 0.8M.

⇒ According to the question: M − C = 0.5 × S.

⇒ M − C = 0.5 × (0.8M) = 0.4M.

⇒ M − 0.4M = C ⇒ 0.6M = C.

⇒ M ÷ C = 1 ÷ 0.6 = 10 ÷ 6 = 5 ÷ 3.

∴ The correct answer is 5 : 3.

Additional Information

Marked Price and Discount

Marked Price (MP) is the price printed on an item. Discount is always calculated on the MP. SP = MP − Discount.

Relationship between CP, SP, and MP

Profit is SP − CP, whereas Discount is MP − SP. To find the ratio between MP and CP, we can use the formula MP ÷ CP = (100 + P%) ÷ (100 − D%) if profit percentage is known.

Shortcut Trick

Initial Ratio (Water : Milk) = 6 : 7

Final Ratio (Water : Milk) = 3 : 5. To make Water constant, multiply final ratio by 2 → 6 : 10.

Increase in Milk = 10 − 7 = 3 units. Given, 3 units = 15 litres → 1 unit = 5 litres.

Initial mixture x = (6 + 7) units = 13 units = 13 × 5 = 65 litres.

∴ The correct answer is 65 litres.

Alternate Method

Given: Initial ratio 6:7, added 15 litres milk, final ratio 3:5.

Formula Used: Ratio × constant = Quantity; Initial Value x = Sum of initial components.

⇒ Let water = 6k and milk = 7k. Total volume x = 13k.

⇒ 6k / (7k + 15) = 3 / 5

⇒ 5 × 6k = 3 × (7k + 15)

⇒ 30k = 21k + 45

⇒ 9k = 45 ⇒ k = 5

⇒ x = 13 × 5 = 65 litres.

∴ The correct answer is 65 litres.

Additional Information

Constant Variable Concept

When only one component is added or removed from a mixture, the quantity of the other component remains constant. Always equate its ratio units first.

Alligation Rule

Used to find the ratio in which two quantities are mixed to get a final concentration: (Higher value − Mean) / (Mean − Lower value).

Replacement Method

Final Quantity = Initial Quantity × (1 − amount replaced/total)ⁿ, where n is the number of times the process is repeated.

Calculations:

Total number of books issued to A in all library together

⇒ 18 + 30 + 24 = 72

Total number of books issued to C in all library together

⇒ 25 + 10 + 32 = 67

So, required difference 72 – 67 = 5

Calculations:

Number of books issued to A in library Q = 30

Number of books issued to B in library Q = 35

Required ratio 30 : 35 = 6: 7

So, x = 7 ⇒  9x = 9 × 7 = 63

Calculations:

Total number of books issued to C in library R = 32

Number of books issued to D in library R:

⇒ 32 × 25/100 + 12

⇒ 8 + 12 = 20