Search Previous Year Questions

Concept Used:

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

Now,

Calculations:

Considering the question

⇒ 3 + 4 – 6 × 12 × 15 ÷ 5

⇒ 3 + 4 – 6 × 180 ÷ 5

⇒ 7 – 6 × 36

⇒ 7 – 216

⇒ – 209

Given:

Principal of Ram = Rs. 8000

Rate of interest (For Ram) = 12%

Principal of Sham = Rs. 9100 

Rate of interest (For Sham) = 10%

Amount of Ram and Sham are equal

Formula used:

SI \(= \frac{{{\rm{P;}} \times {\rm{;R;}} \times {\rm{;T}}}}{{100}}\)

Amount = P + S.I.

Calculation:

Let the required time be y years.

Amount of Ram = Amount of Sham

8000 + [8000 × (12/100) × y] = 9100 + [9100 × (10/100) × y]

⇒ 8000 + 960 y = 9100 + 910 y

⇒ 960 y - 910 y = 9100 - 8000

⇒ 50 y = 1100

⇒ y = 22 years

∴ The time taken to debt become equal is 22 years

Shortcut Trick

Use the weighted average formula to find the overall pass percentage directly.

Total Pass % = (Boys % × Boys Pass Rate + Girls % × Girls Pass Rate) ÷ 100

Total Pass % = (40 × 40 + 60 × 60) ÷ 100

Total Pass % = (1600 + 3600) ÷ 100 = 5200 ÷ 100 = 52%

∴ The correct answer is 52%.

Alternate Method

Given:

⇒ Boys in class = 40%

⇒ Girls in class = 100% − 40% = 60%

⇒ Pass rate among boys = 40%

⇒ Pass rate among girls = 60%

Formula Used:

Number of Passed Students = (Pass % × Total Students) ÷ 100

Calculations:

Let the total number of students in the class be 100.

⇒ Total Boys = 40

⇒ Total Girls = 60

⇒ Boys who passed = 40% of 40 = (40 × 40) ÷ 100 = 16

⇒ Girls who passed = 60% of 60 = (60 × 60) ÷ 100 = 36

⇒ Total students passed = 16 + 36 = 52

⇒ Passed percentage = (52 ÷ 100) × 100 = 52%

∴ The correct answer is 52%.

Additional Information

Weighted Average

When groups of different sizes have different averages, the combined average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Percentage Basics

x% of y is calculated as (x × y) ÷ 100. It is always helpful to assume the total base as 100 for easy calculation.

Ratio Method

The ratio of boys to girls here is 40:60 or 2:3. Total pass percentage = (2 × 40 + 3 × 60) ÷ (2 + 3) = (80 + 180) ÷ 5 = 260 ÷ 5 = 52%.

Given:

Cost of 25 notebooks and 10 books = 425

Calculation:

Let the cost of book is Rs. x

According to question:

Cost of 25 notebooks + cost of 10 book = 425

25(15) + 10x = 425

⇒ 10x = 425 – 375

⇒ 10x = 50

⇒ x = 5

∴ Cost of 1 book is Rs. 5

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

\(\frac{3}{5} \times 2\frac{3}{5} \div ;\frac{{13}}{{15}};of;1\frac{1}{4} + ;\frac{2}{{11}} \times 4\frac{2}{5} \div ;\frac{5}{7};of;3\frac{2}{3}\)

⇒ \(\frac{3}{5} \times \frac{13}{5} \div ;\frac{{13}}{{15}};of ;\frac{5}{4} + ;\frac{2}{{11}} \times \frac{22}{5} \div ;\frac{5}{7};of ;\frac{11}{3}\)

⇒ \(\frac{3}{5} \times \frac{13}{5} \div ;(\frac{{13}}{{15}};\times ;\frac{5}{4}) + ;\frac{2}{{11}} \times \frac{22}{5} \div ;(\frac{5}{7};\times ;\frac{11}{3})\)

⇒ \( \frac{3}{5} \times \frac{13}{5} \times ;\frac{{15}}{{13}};\times ;\frac{4}{5} + ;\frac{2}{{11}} \times \frac{22}{5} \times ;\frac{7}{5};\times ;\frac{3}{11}\)

⇒ \(\frac{36}{25} \ + \ \frac{84}{275}\)

⇒\(\frac{396 \ + \ 84}{275} \)

⇒ \(\frac{480}{275} \)

⇒ \(\frac{96}{55} \)

∴ 96/55

Given:

Ratio of milk and water in mixture = 3 : 2 

The initial quantity of mixture = 13 L

Quantity of mixture replaced = 3 L

Concept used:

While removing some quantity of mixture from a mixture,

The ratio of things present in the mixture remains same.

Calculation:

Mixture remaining after removal of 3 L = 13 - 3 = 10 L

So, quantity of milk = 3/5 × 10 = 6 L

And, quantity of water = 2/5 × 10 = 4 L

Now, quantity of milk after adding 3 L milk = 6 + 3 = 9 L

⇒ Milk :  Water = 9 : 4

∴ Ratio of Milk and water in newly formed mixture is 9 : 4

Given:

\(\sqrt {10 + \sqrt {27 + \sqrt {65 + \sqrt {256} } } }\)

Calculation:

\(\sqrt {10 + \sqrt {27 + \sqrt {65 + \sqrt {256} } } }\)

⇒ \(\sqrt {10 + \sqrt {27 + \sqrt {65 + 16} } } \)

⇒ \(\sqrt {10 + \sqrt {27 + \sqrt {81} } } \)

⇒ \(\sqrt {10 + \sqrt {27 + 9} }\)

⇒ \(\sqrt {10 + \sqrt {36} }\)

⇒ \(\sqrt {10 + 6}\)

⇒ √16

⇒ 4

Given:

Total amount which is divided among A, B and C = Rs. 6,300

X : Y = 7 : 5 and Y : Z = 4 : 3

Calculation:

X : Y = 7 : 5     ----(1)

Y : Z = 4 : 3     ----(2)

Multiply by 4 in equation (1) and multiply by 5 in equation (2)

X : Y : Z = 28 : 20 : 15

Ratio of X : Y : Z = 28x : 20x : 15x

According to the question

28x + 20x + 15x = 6,300

⇒ 63x = 6,300

⇒ x = 6,300/63

⇒ x = 100

∴ Share of Y = 20 × 100 = Rs. 2,000

Given:

Principal = Rs. 40,000

The rate of interest for 3 years = 5%, 8% and 10%

Time = 3 years

Calculation:

According to the question, we have

5% = 1/20

8% = 2/25

10% = 1/10

Now,

5000 units = Rs. 40000

⇒ 1 unit = Rs. 8

6237 units = 8 × 6237

⇒ Rs. 49896

∴ The amount after three years is Rs. 49896.

Traditional Method:

Formula Used:

When rates are different for different years, R₁%, R₂% and R₃% for first years, second year and third year respectively.

Amount = P × {1 + (R₁/100)} × {1 + (R₂/100)} × {1 + (R₃/100)}

Where,

P =Principal

R1%, R2% and R3% = Rate of interest for three years

Calculation:

According to the question, we have

Amount = 40000 × {1 + (5/100)} × {1 + (8/100)} × {1 + (10/100)}

⇒ 40000 × (21/20) × (27/25) × (11/10)

⇒ (40000 × 21 × 27 × 11)/(20 × 25 × 10)

⇒ 8 × 21 × 27 × 11

⇒ 49896

∴ The amount after three years is Rs. 49896.

Let the side of the bigger cube be 2 cm (or as you wish answer will be same in given condition)

Volume of the bigger cube = 2 × 2 × 2 = 8 cm

Let the side of smaller cube be x.

According to the question

⇒ x × 8 = 8

⇒ x = 1 cm

∴ Side of smaller cube be 1 cm.

As we know

Total surface area of the cube = 6 a²

Total surface area of the bigger cube = 6 × 2² = 6 × 4 = 24 cm²

Total surface area of the smaller cube = 6 × 1² = 6

Sum of the surface area of three of the smaller cubes = 3 × 6 = 18

∴ Required ratio = 24 : 18 = 4 : 3