Search Previous Year Questions

Given:

√625 × √400 ÷ 52 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

√625 × √400 ÷ 52 = ?

⇒ 25 × 20 ÷ 25

⇒ 20

∴ The value of ? will be 20.

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

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

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.

Given expression:

\(\Rightarrow \frac{{125}}{{100}} \times 320 + \frac{x}{{100}} \times 125 = 4400\)

\( \Rightarrow \frac{5}{4} \times 320 + x \times \frac{5}{4} = 4400\)

\(\Rightarrow \frac{{5x}}{4} = 4400 - 400\)

⇒ x = 3200

Follow these BODMAS rules to solve the question

Step-1∶ The part of the equation containing 'Brackets' must be solved first, and in the bracket,

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 solved

Step-4∶ At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.

⇒ 25 × 625 ÷ 125 = 500 × 2² ÷ ?

⇒ 5² × 5⁴ ÷ 5³ = 5 × 100 × 2² ÷ ?

⇒ 5² × 5⁴ ÷ 5³ = 5 × 25 × 4 × 2² ÷ ?

⇒ 5² × 5⁴ ÷ 5³ = 5 × 5² × 2² × 2² ÷ ?

⇒ 5^{(2 + 4 – 3)} = 5^{(1 + 2)} × 2⁴ ÷ ?

⇒ 5³ = 5³ × 2⁴ ÷ ?

⇒ ? = 2⁴

⇒ ? = 16

Correct answer is: 3

Concept used:

The BODMAS rule should be followed to solve the question as per the given table:

Calculation:

110 + 1869 ÷ 21 + 53 - 72 = ? + √49

⇒ 110 + (1869/21) + 53 - 49 = ? + 7

⇒ 110 + 89 + 53 - 49 = ? + 7

⇒ 252 - 49 - 7 = ?

⇒ 252 - 56 = ?

⇒ ? = 196

∴The value of ? is 196

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

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket, the BODMAS Rule must be followed,

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.

Given expression is,

⇒ 504 ÷ 18 × 25

⇒ 28 × 25

⇒ 700

Hence the answer is 700.

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

Step-1-Parts 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,

26.5 × ? × 12.7 = 4307.84

⇒ 336.55 × ? = 4307.84

⇒ ? = 12.8

Shortcut Trick

Total Rate × Time = 5% × 8 = 40%.

Total Interest = 40% of X + 40% of (X + 50) = 1020.

40% of (2X + 50) = 1020 ⇒ 2X + 50 = 1020 ÷ 0.4 = 2550.

2X = 2500 ⇒ X = 1250.

∴ The correct answer is ₹1250.

Alternate Method

Given:

Principal 1 (P₁) = ₹X, Principal 2 (P₂) = ₹(X + 50)

Rate (R) = 5%, Time (T) = 8 years, Total Interest = ₹1020

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI₁ + SI₂ = 1020

⇒ [(X × 5 × 8) ÷ 100] + [((X + 50) × 5 × 8) ÷ 100] = 1020

⇒ [40X ÷ 100] + [40(X + 50) ÷ 100] = 1020

⇒ 0.4X + 0.4X + 20 = 1020

⇒ 0.8X = 1020 − 20

⇒ 0.8X = 1000

⇒ X = 1000 ÷ 0.8 = 1250

∴ The correct answer is ₹1250.

Additional Information

Simple Interest Properties

Simple interest remains constant every year as it is always calculated on the original Principal amount.

Effective Rate of Interest

The total interest percentage over a period is the product of Rate and Time (R × T%).

Amount Formula

Total Amount (A) = Principal (P) + Simple Interest (SI) = P[1 + (R × T)/100].

Shortcut Trick

Present ages are in the ratio 3 : 4, while 10 years ago they were 5 : 7.

⇒ Difference in present ratio = 4 − 3 = 1

⇒ Difference in ratio 10 years ago = 7 − 5 = 2

For 10 years, the difference between the ratio parts changes by 1 part.

⇒ 1 part = 10 years

⇒ Present age of B = 4 × 20 = 80 years

∴ The present age of B is 80 years.

Alternate Method

Given:

Present age ratio of A : B = 3 : 4

Age ratio 10 years ago = 5 : 7

Formula Used:

Present ages = 3k and 4k

Calculations:

⇒ 10 years ago, their ages = (3k − 10) and (4k − 10)

⇒ (3k − 10) : (4k − 10) = 5 : 7

⇒ 7(3k − 10) = 5(4k − 10)

⇒ 21k − 70 = 20k − 50

⇒ k = 20

⇒ B's present age = 4 × 20 = 80 years

∴ The present age of B is 80 years.

Required ratio = (360 + 420): (240 + 300) = 780: 540 = 13:9

Average no. of boys participating from Sunday to Wednesday = (240 + 360 + 300 + 420)/4 = 330

Number of boys participating on Thursday = 330 × 120% = 396