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Given:

The merchant gives a discount of 25% on each shirt having cost price of Rs 250

Calculations:

Discount of each shirt = 25% of 250 = 62.5 rupees

He wants a total of 875 rupees as a discount.

So,

Number of shirts he purchased × discount on each shirt = Total discount

Number of shirts × 62.5 = 875

The number of shirts = 875/62.5 = 14

∴ The correct choice will be option 3.

Total number of children in the village D = (20/100) × 2000 = 400

As 70% of the children attend school form village D, we have:

∴ Number of children attending school from village D = (70/100) × 400 = 280

Given:

Selling price of each articles = Rs. 10591

Gain = 19%

Loss = 11%

Calculation:

SP of each articles = Rs. 10591

CP of first article = Rs. (10591 × 100/119)

⇒Rs. 8900

CP of second article = Rs. (10591 × 100/89)

⇒ 11900

Total SP of both the article = 10591 × 2 = 21182

Total CP of both the article = 8900 + 11900 = 20800

Total Gain = 21182 – 20800 = 382

Gain percentage = (382/20800 × 100)

⇒ 1.83%

∴ His overall Profit percentage is 1.8%

Concept Used:

A vulgar fraction, common fraction or fraction is a fraction written in the usual way which is one number (integer) above another (integer) separated by a line.

Calculation:

\(0.2\overline{34}+0.\overline{29}\)

Convert \(0.2\overline{34}\) into a vulgar fraction

x = 234 - 2 /990 = 232/990

Convert \(0.\overline{29}\) into a vulgar fraction

y = 29/99

Add the fractions

(232/990) + (29/99)

Find LCM of 990 and 99, which is 990:

(232/990) + (290/990) = 522/990

Simplify:

522/990 = 29/55

Final Answer:

29/55.

When a moving body travels at two different speeds of x km/hr and y km/hr, the average speed of the journey = 2xy/(x + y)

Let x = 48 km/hr. and y = 72 km/hr.

⇒ Average speed of the bus = (2 × 48 × 72)/(48 + 72) = 6912/120 = 57.6 km/hr.

Time taken in journey = 2.5 hrs.

∵ Average speed = Total distance travelled/Total time taken

∴ Distance travelled by bus = 57.6 × 2.5 = 144 km

Shortcut Trick

Total Selling Price (SP) = (100% − 6%) + (100% − 10%) + (100% − 12%) = 272% of MP

⇒ 272% of MP = ₹6,800

⇒ MP = 6800 × 100 ÷ 272

⇒ MP = ₹2,500

∴ The correct answer is ₹2,500.

Alternate Method

Given:

Discount on 1^st, 2^nd, and 3^rd fan = 6%, 10%, and 12% respectively

Total amount paid for 3 fans = ₹6,800

Note: The 8% discount for a single fan purchase is irrelevant to this 3-fan scenario.

Formula Used:

Selling Price (SP) = Marked Price (MP) × (100 − Discount%) ÷ 100

Calculations:

Let the Marked Price of each fan be MP.

⇒ SP of 1^st fan = MP × (100 − 6)% = 0.94 MP

⇒ SP of 2^nd fan = MP × (100 − 10)% = 0.90 MP

⇒ SP of 3^rd fan = MP × (100 − 12)% = 0.88 MP

⇒ Total SP for 3 fans = 0.94 MP + 0.90 MP + 0.88 MP = 2.72 MP

⇒ We are given that the total selling price is ₹6,800.

⇒ 2.72 MP = 6800

⇒ MP = 6800 ÷ 2.72

⇒ MP = 680000 ÷ 272 = ₹2,500

∴ The correct answer is ₹2,500.

Additional Information

Marked Price (MP) and Discount

Discount is always calculated on the Marked Price (also known as Tag Price or List Price). SP = MP − Discount.

Successive Discounts

If two successive discounts of a% and b% are given, the equivalent single discount is (a + b − a×b/100)%.

Mark-up Percentage

The percentage by which the MP is raised above the Cost Price (CP). MP = CP × (100 + Mark-up%) ÷ 100.

Shortcut Trick

Initial Ratio of Sugar : Flour = 17 : 28 (Total units = 17 + 28 = 45)

Given 45 units = 27 kg → 1 unit = 27 ÷ 45 = 0.6 kg

To keep Sugar constant at 17 units, multiply final ratio (2 : 5) by 8.5 → 17 : 42.5

Extra Flour added = 42.5 − 28 = 14.5 units

Quantity of added Flour = 14.5 × 0.6 = 8.7 kg

∴ The correct answer is 8.7 kg.

Alternate Method

Given: Initial Sugar : Flour = 17 : 28, Total Weight = 27 kg, Final Ratio = 2 : 5.

⇒ Total initial units = 17 + 28 = 45 units

⇒ Quantity of Sugar = (17 ÷ 45) × 27 = 10.2 kg

⇒ Quantity of Flour = (28 ÷ 45) × 27 = 16.8 kg

⇒ Let added Flour be x kg. New ratio of Sugar : Flour is 2 : 5

⇒ 10.2 ÷ (16.8 + x) = 2 ÷ 5

⇒ 5 × 10.2 = 2 × (16.8 + x)

⇒ 51 = 33.6 + 2x

⇒ 2x = 51 − 33.6 = 17.4

⇒ x = 17.4 ÷ 2 = 8.7 kg

∴ The correct answer is 8.7 kg.

Additional Information

Ratio Constant Property

When one component is added to a mixture, the quantity of the other component remains unchanged. Use this to equate the constant part across different ratios.

Unitary Method in Ratios

Always find the value of 1 unit by dividing the total weight by the sum of ratio parts (Total weight ÷ (a + b)).

Shortcut Trick

Identify the highest common factor: All numbers are multiples of 47.

94 = 47 × 2, 188 = 47 × 4, 235 = 47 × 5.

LCM = 47 × LCM(2, 4, 5) = 47 × 20.

LCM = 940.

∴ The correct answer is 940.

Alternate Method

Given: Numbers are 94, 188, and 235.

Formula Used: Prime Factorization Method for LCM.

⇒ 94 = 2¹ × 47¹

⇒ 188 = 2² × 47¹

⇒ 235 = 5¹ × 47¹

⇒ LCM = 2² × 5¹ × 47¹

⇒ LCM = 4 × 5 × 47

⇒ LCM = 20 × 47 = 940.

∴ The correct answer is 940.

Additional Information

LCM (Least Common Multiple)

The smallest positive integer that is divisible by each of the given numbers. It is calculated by taking the highest power of every prime factor present.

HCF and LCM Relation

For two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Prime Factorization

Expressing a number as a product of prime numbers to easily find common divisors or multiples.

GIVEN:

P = Rs. 6,000, R = 3%, SI = Rs. 240, T = ?

FORMULAE USED:

SI = PRT/100

CALCULATION:

⇒ 240 = 6000 × T × 3%

⇒ 240 = 180T

⇒ T = 4/3 years

⇒ T = (4/3) × 12 months

⇒ T = 16 months

∴ Rohan will pay the debt after 16 months.

Let the incomes of A and B be 3x and 2x respectively.

Income = expenditure + savings

3x = 14000 + 4000

⇒ x = 6000

2x = 12000

Savings of B = 12000 – 10,000 = 2000