Search Previous Year Questions

Given:

The value of 1.\(\overline{36}\) + 3.\(\overline{24}\) + 1.\(\overline{33}\) is:

Formula used:

To convert a repeating decimal into a fraction:

If the repeating part is "x", use the formula: \(\text{Number} = \frac{\text{Non-repeating + Repeating}}{\text{Denominator}}\)

Calculation:

1.\(\overline{36}\) = 1 + \(\frac{36}{99}\) = \(\frac{135}{99}\)

3.\(\overline{24}\) = 3 + \(\frac{24}{99}\) = \(\frac{321}{99}\)

1.\(\overline{33}\) = 1 + \(\frac{33}{99}\) = \(\frac{132}{99}\)

Now, summing them up:

⇒ 1.\(\overline{36}\) + 3.\(\overline{24}\) + 1.\(\overline{33}\) = \(\frac{135}{99} + \frac{321}{99} + \frac{132}{99}\)

⇒ \(\frac{135 + 321 + 132}{99} = \frac{588}{99}\)

⇒ Simplify: \(\frac{588}{99} = \frac{196}{33}\)

∴ The correct answer is option (4).

Given:

Length of the field (L) = 120 m

Width of the field (W) = 50 m

Formula used:

Perimeter of rectangle = 2 × (L + W)

Diagonal of rectangle = √(L² + W²)

Ratio = Perimeter / Diagonal

Calculation:

Perimeter = 2 × (120 + 50)

⇒ Perimeter = 2 × 170

⇒ Perimeter = 340 m

Diagonal = √(120² + 50²)

⇒ Diagonal = √(14400 + 2500)

⇒ Diagonal = √16900

⇒ Diagonal = 130 m

Ratio = Perimeter / Diagonal

⇒ Ratio = 340 / 130

⇒ Ratio = 2.62

∴ The correct answer is option (2).

Given:

The dealer claims to sell at cost price but uses 945 grams instead of 1 kilogram (1000 grams).

Formula used:

Gain Percentage = Profit/Cost Price × 100

Profit = Selling Price - Cost Price

Calculation:

Cost Price for 1000 grams = ₹1000

Weight actually given = 945 grams

Selling Price for 945 grams = ₹1000

Cost Price for 945 grams = 945/1000 × ₹1000 = ₹945

Profit = Selling Price - Cost Price

⇒ Profit = ₹1000 - ₹945 = ₹55

Gain Percentage = Profit/Cost Price × 100

⇒ Gain Percentage = 55/945 × 100

⇒ Gain Percentage = 5.82%

∴ The correct answer is option (4).

Given:

The price of an article is reduced by 10% and its daily sale increased by 15%.

Formula used:

Net percentage effect = (x + y + (x × y)/100)

Where:

x = percentage change in price = -10%

y = percentage change in daily sale = +15%

Calculation:

⇒ Net effect = (-10) + 15 + ((-10) × 15)/100

⇒ Net effect = 5 + (-150)/100

⇒ Net effect = 5 - 1.5

⇒ Net effect = 3.5% increase

∴ The correct answer is option (4).

Given:

Amount (A) = ₹40,84,101

Rate (r) = 20% per annum

Time (t) = 15 months (1.25 years)

Compounding frequency = Quarterly

Formula used:

A = P(1 + r/(100 × n))^n×t

Where,

A = Amount

P = Principal

r = Rate of interest per annum

n = Number of times compounding in a year

t = Time in years

Calculations:

₹40,84,101 = P(1 + 20/(100 × 4))^4×1.25

⇒ ₹40,84,101 = P(1 + 20/400)⁵

⇒ ₹40,84,101 = P(1 + 0.05)⁵

⇒ ₹40,84,101 = P(1.05)⁵

⇒ ₹40,84,101 = P × 1.276281

⇒ P = ₹40,84,101 / 1.276281

⇒ P = ₹32,00,000

∴ The correct answer is option (3).

Given:

Outer diameter of the spherical shell = 18 cm

Inner diameter of the spherical shell = 12 cm

π = 3.14

Formula Used:

Volume of a sphere = (4/3) × π × r³

Volume of the spherical shell = Volume of outer sphere - Volume of inner sphere

Calculations:

Outer radius (R) = 18/2 = 9 cm

Inner radius (r) = 12/2 = 6 cm

Volume of outer sphere = (4/3) × 3.14 × 9³

⇒ Volume of outer sphere = (4/3) × 3.14 × 729

⇒ Volume of outer sphere = 3052.08 cm³

Volume of inner sphere = (4/3) × 3.14 × 6³

⇒ Volume of inner sphere = (4/3) × 3.14 × 216

⇒ Volume of inner sphere = 904.32 cm³

Volume of the spherical shell = Volume of outer sphere - Volume of inner sphere

⇒ Volume of the spherical shell = 3052.08 - 904.32

⇒ Volume of the spherical shell = 2147.76 cm³

∴ The correct answer is option (2).

Given:

A policeman starts to chase a thief. When the thief goes 12 steps, the policeman moves 9 steps.

6 steps of the policeman = 9 steps of the thief.

Formula used:

Speed = Distance / Time

To find the ratio of the speed of the thief to that of the policeman:

Speed of thief / Speed of policeman = (Distance covered by thief in 1 step) / (Distance covered by policeman in 1 step).

Calculation:

Let the distance covered by the thief in 1 step = T and the distance covered by the policeman in 1 step = P.

6P = 9T

⇒ P / T = 9 / 6

⇒ P / T = 3 / 2

In the given time, the thief takes 12 steps, and the policeman takes 9 steps:

Speed of thief / Speed of policeman = (12 × T) / (9 × P)

⇒ Speed of thief / Speed of policeman = (12 × T) / (9 × (3T / 2))

⇒ Speed of thief / Speed of policeman = (12) / (9 × 3 / 2)

⇒ Speed of thief / Speed of policeman = (12 × 2) / (27)

⇒ Speed of thief / Speed of policeman = 24 / 27

⇒ Speed of thief / Speed of policeman = 8 / 9 = 8 : 9

∴ The correct answer is  8 : 9

Given:

Weight of first type of salt = 5 kg

Cost of first type of salt per kg = Rs. 21

Weight of second type of salt = 3 kg

Cost of second type of salt per kg = Rs. 25

Formula used:

Average cost per kg = (Total cost of mixture) / (Total weight of mixture)

Calculation:

Total cost of mixture = (Weight of first salt × Cost of first salt per kg) + (Weight of second salt × Cost of second salt per kg)

⇒ Total cost = (5 × 21) + (3 × 25)

⇒ Total cost = 105 + 75

⇒ Total cost = 180

Total weight of mixture = 5 + 3 = 8 kg

Average cost per kg = Total cost / Total weight

⇒ Average cost per kg = 180 / 8

⇒ Average cost per kg = 22.5

∴ The correct answer is option (3).

Given:

Marked price (MP) = ₹7,200

Cost price (CP) = 70% below the marked price

Successive discounts = 25% and 25%

Further discount = 18% on net payment

Formula used:

Cost Price (CP) = MP × (1 - Discount %)

Successive Discount = MP × (1 - First Discount %) × (1 - Second Discount %)

Further Discount = SP × (1 - Discount %)

Profit Percentage = [(SP - CP) / CP] × 100

Calculations:

Cost Price:

⇒ CP = 7200 × (1 - 70/100)

⇒ CP = 7200 × 0.3 = ₹2,160

Selling Price after successive discounts:

⇒ SP after first two discounts = 7200 × (1 - 25/100) × (1 - 25/100)

⇒ SP after first two discounts = 7200 × 0.75 × 0.75

⇒ SP after first two discounts = ₹4,050

Selling Price after further discount:

⇒ Final SP = SP after first two discounts × (1 - 18/100)

⇒ Final SP = 4050 × 0.82

⇒ Final SP = ₹3,321

Profit Percentage:

⇒ Profit = Final SP - CP

⇒ Profit = 3321 - 2160 = ₹1,161

⇒ Profit Percentage = (Profit / CP) × 100

⇒ Profit Percentage = (1161 / 2160) × 100

⇒ Profit Percentage ≈ 53.75% = 54%

∴ The correct answer is 54%

Given:

6 men and 4 boys can finish a work in 20 days.

4 men and 6 boys can finish the same work in 24 days.

We need to find the number of days 2 boys and 1 man can finish the work.

Formula used:

Work = (Efficiency × Time)

Efficiency of a group = Total work / Time

Calculation:

Let the efficiency of 1 man be m and 1 boy be b.

Total work = Efficiency × Time

For 6 men and 4 boys:

Work = Efficiency × Time

⇒ (6m + 4b) × 20

⇒ Total work = 120m + 80b

For 4 men and 6 boys:

Work = Efficiency × Time

⇒ (4m + 6b) × 24

⇒ Total work = 96m + 144b

Equating the two total works:

⇒ 120m + 80b = 96m + 144b

⇒ 24m = 64b

⇒ m = 64b / 24

⇒ m = 8b / 3

Now, find the efficiency of 2 boys and 1 man:

Efficiency = (1m + 2b)

⇒ Efficiency = (8b / 3) + 2b

⇒ Efficiency = (8b / 3) + (6b / 3)

⇒ Efficiency = 14b / 3

Total work from the first case:

Total work = (6m + 4b) × 20

⇒ Total work = 120m + 80b

Substitute m = 8b / 3:

⇒ Total work = 120(8b / 3) + 80b

⇒ Total work = (960b / 3) + (240b / 3)

⇒ Total work = 1200b / 3

⇒ Total work = 400b

Time for 2 boys and 1 man:

Time = Total work / Efficiency

⇒ Time = 400b / (14b / 3)

⇒ Time = (400b × 3) / 14b

⇒ Time = 1200 / 14

⇒ Time = 85.7 days

∴ The correct answer is option (3).