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Given:

11² + 120 ÷ 12 × 2 = ? – 30

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

11² + 120 ÷ 12 × 2 = ? – 30

⇒ 121 + 10 × 2 = ? - 30 

⇒ 121 + 20 = ? - 30 

⇒ ? = 141 + 30 = 171

⇒ ? = 171

∴ The value of ? is 171.

Given:

25% of 28 - 20% of 30 + 22 = 5 × ?

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

25% of 28 - 20% of 30 + 22 = 5 × ?

⇒ 28 × (25/100) - 30 × (20/100) + 4 = 5 × ?

⇒ 28 × (1/4) - 30 × (1/5) + 4 = 5 × ?

⇒ 7 - 6 + 4 = 5 × ?

⇒ 5 = 5 × ?

⇒ ? = 1

∴ 1 will come in place of the question mark ('?').

Sale of headphones by T&T in 2020 = (150/100)× 800 = 1200

Sale of charger by T&T in 2020 = (70/100)× 300=210

Hence, total sale = 1200+210 = 1410

Number of Charger sold by M in 2020 = (135/100)× 500 = 675

Number of Charger sold by I in 2020 = (120/100)× 150 = 180

Number of Charger sold by J in 2020 = (120/100)× 200 = 240

Number of Charger sold by K in+ 2020 = (120/100)× 300 = 360

Hence, required percentage will be = [675 / (180+240+360)]× 100=86.53 = 87% (approx.)

Number of adaptors sold in 2020 by M = (140/100)× 250 = 350

Number of headphones sold in 2020 by M = (150/100)× 500 = 750

So, new ratio will be = 750 : 350 = 15:7

Total number of headphones sold in 2019 = 500 + 650 + 750 + 800 + 500 = 3200

Total number of headphones sold in 2020 = (220/100) ×  3200 = 7040

As the sales of other shops are same except M and L.

So, number of headphones sold in 2020 from I, J, and K = 500 + 650 + 750 = 1900

So, number of headphones sold in 2020 from M and L = 7040 – 1900 = 5140

Number of headphones sold in 2020 by M = 5140/2 = 2570

Hence, the total number of headphones sold by M in 2019 and 2020 = 500 + 2570 = 3070

As per data.

Total number of headphones sold in 2019 = 500+650+750+800+500=3200

Total number of the Chargers sold in 2019 = 150+200+300+400+500=1550

Hence, required ratio = 3200:1550 = 320:155 = 64:31

Shortcut Trick

Ratio of Upstream speed to Downstream speed = (Distance_up ÷ Time_up) : (Distance_down ÷ Time_down)

Ratio = (36 ÷ 2) : (30 ÷ 1) = 18 : 30 = 3 : 5

Let Upstream speed = 3k and Downstream speed = 5k. Boat speed = (3k + 5k) ÷ 2 = 4k

Given 4k = 12 kmph ⇒ k = 3. Stream speed = (5k − 3k) ÷ 2 = k = 3 kmph

∴ The correct answer is 3 kmph.

Alternate Method

Given: Speed of boat in still water (u) = 12 kmph. Let speed of stream = v kmph.

Formula: Upstream Speed (S_u) = u − v | Downstream Speed (S_d) = u + v | Time = Distance ÷ Speed

⇒ Time Upstream (T_u) = 36 ÷ (12 − v)

⇒ Time Downstream (T_d) = 30 ÷ (12 + v)

⇒ Ratio T_u : T_d = 2 : 1

⇒ [36 ÷ (12 − v)] ÷ [30 ÷ (12 + v)] = 2 / 1

⇒ [36 × (12 + v)] ÷ [30 × (12 − v)] = 2 / 1

⇒ 6 × (12 + v) = 10 × (12 − v)

⇒ 72 + 6v = 120 − 10v

⇒ 16v = 48

⇒ v = 3 kmph

∴ The correct answer is 3 kmph.

Additional Information

Upstream and Downstream Speed

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

Speed of Boat in Still Water

It can be calculated from the given speeds as: u = (Downstream Speed + Upstream Speed) ÷ 2.

Speed of Stream

It can be calculated as: v = (Downstream Speed − Upstream Speed) ÷ 2.

Shortcut Trick

Base of triangle = (2 × Area) ÷ Height = (2 × 168) ÷ 24 = 14 cm.

Given, Breadth of rectangle (b) = Base of triangle = 14 cm.

Length (l) = (Perimeter ÷ 2) − b = (84 ÷ 2) − 14 = 42 − 14 = 28 cm.

∴ The correct answer is 28 cm.

Alternate Method

Given: Height (h) = 24 cm, Area = 168 cm², Perimeter (P) = 84 cm.

Formula Used: Area of triangle = (1/2) × base × height; Perimeter of rectangle = 2(l + b).

⇒ 168 = (1/2) × Base × 24

⇒ 168 = Base × 12

⇒ Base = 168 ÷ 12 = 14 cm

⇒ Breadth (b) of rectangle = 14 cm

⇒ 2(l + 14) = 84

⇒ l + 14 = 42

⇒ l = 42 − 14 = 28 cm

∴ The correct answer is 28 cm.

Additional Information

Area of Rectangle

The total region covered by a rectangle in a 2D plane is calculated as Length × Breadth (l × b).

Right-Angled Triangle Area

If the triangle is right-angled, the area is simply half the product of the two sides containing the right angle.

Semi-perimeter of Rectangle

The sum of length and breadth (l + b) is equal to half of the perimeter (P ÷ 2).

Shortcut Trick

Ratio of Income = 7 : 5 (Gap = 2 units)

Ratio of Expenditure = 5 : 3 (Gap = 2 units)

Since the gap between Income and Expenditure is same for both (7−5 = 2 and 5−3 = 2), then 2 units = ₹10,000.

1 unit = ₹5,000.

Sum of Income = (7 + 5) = 12 units → 12 × 5,000 = ₹60,000.

∴ The correct answer is ₹60000.

Alternate Method

Given: Ratio of Incomes = 7 : 5, Ratio of Expenditures = 5 : 3, Savings = ₹10,000 each.

Formula Used: Income − Expenditure = Savings

⇒ Let Incomes be 7x and 5x.

⇒ (7x − 10000) / (5x − 10000) = 5 / 3

⇒ 3(7x − 10000) = 5(5x − 10000)

⇒ 21x − 30000 = 25x − 50000

⇒ 4x = 20000

⇒ x = 5000

⇒ Total Income = 7x + 5x = 12x = 12 × 5000 = 60000

∴ The correct answer is ₹60000.

Additional Information

Income-Expenditure Concept

Always remember the basic relationship: Income = Expenditure + Savings. If savings are equal, the difference between ratio terms of income and expenditure must be made equal.

Cross Multiplication Method

For different savings, use: (I₁ × E₂ − I₂ × E₁) units = (S₁ × E₂ − S₂ × E₁) to find the value of one unit directly.

Ratio Balancing

If the difference between Income parts and Expenditure parts is not equal, multiply the ratios by the difference of the other ratio to balance them.