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Suppose x will come in place of question mark;

5350 – 50 × 3139 ÷ 73 = x × 64

Applying BODMAS Rule;

⇒ 5350 – 50 × 43 = 64x

⇒ 5350 – 2150 = 64x

⇒ 3200 = 64x

⇒ x = 50

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1 - steps of an equation enclosed in ‘Brackets’ must be solved first.

Step - 2 - any mathematical ‘Of’ or ‘Exponent’ must be solved next.

Step - 3 - Next, the parts of the equation that contain ‘Division’ and ‘Multiplication’ are calculated.

Step - 4 - Last but not least, the parts of the equation that contain ‘Addition’ and ‘Subtraction’ should be calculated.

Now, the given expression:

⇒ (224 ÷ 16 × 33) ÷ 21 = 2 × (? + 3)

⇒ (14 × 33) ÷ 21 = 2 × (? + 3)

⇒ 462 ÷ 21 = 2 × ? + 6

⇒ 22 = 2 × ? + 6

⇒ 2 × ? = 22 - 6

⇒ 2 × ? = 16

⇒ ? = 8

Shortcut Trick

Effective Rate of Interest for 2 years at 2% = r + r + (r × r)/100 = 2 + 2 + (2 × 2)/100 = 4.04%.

Given Compound Interest (CI) = ₹323.2.

Equating percentage to value: 4.04% of Principal = ₹323.2.

Principal = 323.2 ÷ 0.0404 = ₹8,000.

∴ The correct answer is ₹8,000.

Alternate Method

Given:

Time (T) = 2 years

Rate (R) = 2% per annum

Compound Interest (CI) = ₹323.2

Formula Used:

CI = P[(1 + R/100)^T − 1]

Calculations:

⇒ 323.2 = P[(1 + 2/100)² − 1]

⇒ 323.2 = P[(1.02)² − 1]

⇒ 323.2 = P[1.0404 − 1]

⇒ 323.2 = P × 0.0404

⇒ P = 323.2 ÷ 0.0404

⇒ P = 3232000 ÷ 404

⇒ P = ₹8,000

∴ The correct answer is ₹8,000.

Additional Information

Effective Interest Rate

For 2 years, the net effective rate for CI is given by x + y + (xy/100). For 2%, it is 2 + 2 + 0.04 = 4.04%.

Difference between CI and SI

The difference for 2 years is P(R/100)². Here, the difference would be ₹8000 × (0.0004) = ₹3.2.

Amount Formula

Total Amount (A) = Principal (P) + Compound Interest (CI). Also, A = P(1 + R/100)^T.

Shortcut Trick

Proportion of alcohol in Mixture 1 = 7/10 and Mixture 2 = 3/8.

Mixed in ratio 3 : 4 → Total parts = 3 + 4 = 7 units.

Total alcohol in 7 units = [3 × (7/10)] + [4 × (3/8)] = 2.1 + 1.5 = 3.6 units.

Alcohol fraction in final mix = 3.6 / 7.

Alcohol in 70 litres = (3.6 / 7) × 70 = 36 litres.

∴ The correct answer is 36 litres.

Alternate Method

Given: Ratio in Mix 1 = 7 : 3, Ratio in Mix 2 = 3 : 5, Mixing ratio = 3 : 4, Total quantity = 70 litres.

Formula: Total Alcohol = Σ(Quantity × Alcohol Fraction)

⇒ Quantity of Mix 1 = [3 / (3 + 4)] × 70 = 30 litres.

⇒ Quantity of Mix 2 = [4 / (3 + 4)] × 70 = 40 litres.

⇒ Alcohol from Mix 1 = 30 × (7 / (7 + 3)) = 30 × (7/10) = 21 litres.

⇒ Alcohol from Mix 2 = 40 × (3 / (3 + 5)) = 40 × (3/8) = 15 litres.

⇒ Total Alcohol = 21 + 15 = 36 litres.

∴ The correct answer is 36 litres.

Additional Information

Alligation Method

Used to find the ratio in which two ingredients at given prices/concentrations must be mixed to produce a mixture of a desired price/concentration.

Fractional Mixing

When mixing two ratios A:B and C:D in ratio m:n, ensure the sum of parts (A+B and C+D) are made equal or scaled to m and n respectively before adding.

Calculation

Sunday total = 84 + 55 + 64 = 203

Monday total = 48 + 32 + 32 = 112

Difference = 203 – 112 = 91

Calculation

Given: Average (B + C + D)/3 = 42

→ B + C + D = 42 × 3 = 126

B + C = 50 + 48 = 98 → D = 126 – 98 = 28

Shop A on Tuesday = 56

Difference = 56 – 28 = 28 cakes

Calculation

Given: Shop C on Wednesday = 48

Ratio C (Wed) : C (Thu) = 4 : 5

→ C (Thu) = (48 × 5)/4 = 60

Shop B (Thu) = C (Thu) + 19 = 60 + 19 = 79 cakes

Calculation

Shop A (Tue + Wed) = 56 + 70 = 126

Shop C Wed = 48

Ratio = 126 : 48

→ 21 : 8

Calculation

Shop C Monday = 32, Wednesday = 48

Difference = 48 – 32 = 16

Percentage less = (16 ÷ 48) × 100 = 33.33%

Shortcut Trick

Let the total distance be 3x km. Bus distance = 2x, Bicycle distance = x.

Total time = (Distance₁ ÷ Speed₁) + (Distance₂ ÷ Speed₂)

⇒ 3 = (2x ÷ 60) + (x ÷ 30) ⇒ 3 = (x ÷ 30) + (x ÷ 30) ⇒ 3 = 2x ÷ 30

⇒ x = (3 × 30) ÷ 2 = 45 km.

∴ The correct answer is 45 km.

Alternate Method

Given: Bus Speed = 60 km/hr, Bicycle Speed = 30 km/hr, Total Time = 3 hours.

Formula: Time = Distance ÷ Speed

Let total distance be D.

⇒ Time taken by bus = (2D/3) ÷ 60 = 2D ÷ 180 = D ÷ 90

⇒ Time taken by bicycle = (D/3) ÷ 30 = D ÷ 90

⇒ Total Time = (D ÷ 90) + (D ÷ 90) = 3

⇒ 2D ÷ 90 = 3

⇒ D = (3 × 90) ÷ 2 = 135 km

⇒ Distance by bicycle = (1/3) × 135

∴ The correct answer is 45 km.

Additional Information

Average Speed Formula

When a distance is divided into parts, Average Speed = Total Distance ÷ Total Time.

Time, Speed, Distance Relationship

For a constant distance, speed is inversely proportional to time (S₁/S₂ = T₂/T₁).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.