Answer: Option B. -> 2011
 -    Suppose commodity X will cost 40 paise more than Y after z years.
  Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40
   0.25z = 0.40 + 2.10
 z = 2.50 = 250 = 10. 0.25 25
  X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.

Answer: Option C. -> 49.97592

 -     4083 x 102 x 12 = 4997592. Sum of decimal places = 5         40.83 x 1.02 x 1.2 = 49.97592.    

Multiplication is a basic arithmetic operation in mathematics that is used to find the product of two or more numbers.

To multiply decimal numbers, we can follow these steps:

Multiply the numbers as if they were whole numbers, ignoring the decimal points.

Count the total number of digits to the right of the decimal point in the original numbers.

Insert the decimal point into the answer by starting from the right and counting as many digits as the total from step 2.

Applying this method to the given numbers, we get:

40.83

x 1.02

x 1.2

499.7592

There are 5 digits to the right of the decimal point in the original numbers (2 in 1.02 and 1 in 1.2, totaling to 3).

Starting from the right, we count 5 digits and insert the decimal point, giving us the final answer of 49.97592.

Therefore, the correct option is C, 49.97592.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option A. -> 5/3

 -   Given expression = (0.2 x 0.2 + 0.01) = 0.04 + 0.01 = 0.05 = 5 (0.1 x 0.1 + 0.02) 0.01 + 0.02 0.03 3

To solve the expression (0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)-1, we can use the order of operations (PEMDAS) and simplify step by step:

Step 1: Simplify the terms inside the parentheses:

(0.2 x 0.2 + 0.01) = 0.045

(0.1 x 0.1 + 0.02) = 0.012

Step 2: Raise the expression inside the parentheses to the power of -1 (or take the reciprocal):

(0.045) (0.012)-1 = (0.045) (83.33...) = 3.75

Step 3: Simplify the final result by dividing by 2:

3.75 / 2 = 1.875

Therefore, the answer is not one of the given options. However, we can check our calculations and see that we made a mistake in step 2. We need to raise the entire expression to the power of -1, not just the second term inside the parentheses:

(0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)-1 = (0.045) (0.012)-1

Using the formula a-n = 1/an, we can rewrite the expression as:

(0.045) / (0.012)

Simplifying, we get:

(0.045) / (0.012) = 3.75

Finally, we divide by 2 to get the correct answer:

3.75 / 2 = 1.875

Therefore, the correct option is not given. However, we can simplify the expression further:

(0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)-1

= (0.04 + 0.01) (0.01 + 0.02)-1

= 0.05 (0.03)-1

= 5/3

Therefore, the correct answer is option A, 5/3.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> 1.6416
 -   Given expression = 2 x 4 x 8 x 16 + 4 x 8 x 16 + 8 x 16 + 16 +1 2 x 4 x 8 x 16           Given expression = 1024 + 512 + 128 + 16 + 1 1024 = 1681 1024  = 1.6416  

Answer: Option C. -> 100.9
 -   4.036 0.04 = 403.6 4  = 100.9

Answer: Option B. -> 1
 -   Given expression = (a2 - b2) (a + b)(a - b) = (a2 - b2) (a2 - b2)  = 1

Answer: Option A. -> 1/100
 -   Given expressoion = (96.54 - 89.63) (96.54 + 89.63) x (9.654 + 8.963) (965.4 - 896.3)         = (96.54 - 89.63) (965.4 - 896.3) x (9.654 + 8.963) (96.54 + 89.63)         = (96.54 - 89.63) 10 (96.54 - 89.63) x (96.54 + 89.63) 10 (96.54 + 89.63)         = 1 10 x 1 10 = 1 100            

Answer: Option B. -> 23/800

 -   0.00625 of 23 = 625 x 23 = 23 5 100000 5 800

To express 0.00625 of 23/5 as a vulgar fraction, we need to perform the following calculations:

0.00625 × 23/5 = (625/100000) × (23/5) [Converting 0.00625 to fraction form]

= 14375/500000

= 23/800 [Simplifying the fraction by dividing the numerator and denominator by 625]

Therefore, the answer is Option B, 23/800.

Now, let's understand the solution in detail:

• A vulgar fraction is a fraction where the numerator and denominator have no common factors other than 1. It is also called a simple fraction or a common fraction.
• To convert a decimal to a fraction, we need to count the number of decimal places and write the decimal as the numerator over 1 followed by the same number of zeros as the decimal places. For example, 0.25 can be written as 25/100 or 1/4.
• To multiply fractions, we simply multiply the numerators together and multiply the denominators together. For example, (a/b) × (c/d) = (ac/bd).
• To simplify a fraction, we divide both the numerator and denominator by their greatest common factor. For example, 6/12 can be simplified to 1/2 by dividing both the numerator and denominator by 6.
• In the given problem, we need to multiply 0.00625 with 23/5 and express the result as a vulgar fraction. To do this, we first convert 0.00625 to fraction form by writing it as 625/100000. We then multiply it with 23/5 to get 14375/500000.
• To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 625. This gives us 23/800 as the final answer.
• Therefore, the correct answer is Option B, 23/800.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> 629.6357
 -   617    6.017    0.617 -   6.0017 629.636

Answer: Option C. -> 4/5
 -   3 = 0.75,    5 = 0.833,    1 = 0.5,    2 = 0.66,    4 = 0.8,    9 = 0.9. 4 6 2 3 5 10
  Clearly, 0.8 lies between 0.75 and 0.833.
  4   lies between   3   and   5 . 5 4 6