Explanation : 

If 1 litre of water weighs 1kg ….

GIVEN CONVERSIONS:
1. Volume Conversion:
– 1 cubic millimeter = 10^-6 liters
– 1 liter = 10^6 cubic millimeters

2. Weight-Volume Relationship:
– 1000 grams (1 kg) = 10^6 cubic millimeters

CALCULATION:
1. To find volume for 0.1 grams:
– If 1000 grams = 10^6 cubic millimeters
– Then 1 gram = 10^3 cubic millimeters
– Therefore, 0.1 grams = 10^2 cubic millimeters
– 0.1 grams = 100 cubic millimeters

Explanation : 

C is younger than D

From statement S1 we know that C is younger than D but older than A and B. So the order of their ages is: D > C > A and B.

From statement S3 we know that A is older than B. Combining this information with statement S1, we get the order of their ages as: D > C > A > B.

So from statements S1 and S3 together, we can conclude that B is the youngest among A, B, C and D

Explanation : 

Digit n > 3 is divisible by 3

Since n is divisible by 3 but not divisible by 6, it means that n must be an odd multiple of 3. Let’s take n=9 as an example.

(a) 2n = 2 * 9 = 18 which is not divisible by 4

(b) 3n = 3 * 9 = 27 which is not divisible by 4

(c) 2n +4 = (2 *9) +4 =22 which is not divisible by 4

(d) 3n +1 = (3 *9)+1=28 which is divisible by 4

So the correct answer is (d) 3n+1.

Explanation : 

Let’s solve this step by step:

PROBLEM: Finding which fraction has minimum change when s is added to both numerator and denominator

ORIGINAL FRACTIONS:
2/3, 3/4, 4/5, 5/6

NEW FRACTIONS AFTER ADDING s:
(2 + s)/(3 + s)
(3 + s)/(4 + s)
(4 + s)/(5 + s)
(5 + s)/(6 + s)

CHANGES IN VALUE:
|2/3 – (2 + s)/(3 + s)|
|3/4 – (3 + s)/(4 + s)|
|4/5 – (4 + s)/(5 + s)|
|5/6 – (5 + s)/(6 + s)|

ANALYSIS:
1. When s becomes very large:
– The numerator terms (2,3,4,5) become negligible
– The denominator terms (3,4,5,6) become negligible
– All fractions approach s/s = 1

2. Original values:
2/3 ≈ 0.667
3/4 = 0.750
4/5 = 0.800
5/6 ≈ 0.833

3. Since all fractions approach 1:
– The fraction closest to 1 will have minimum change
– 5/6 is closest to 1 among all given fractions

CONCLUSION: The fraction 5/6 will have the minimum change in value when s is added to both numerator and denominator.

Explanation :

Remainder when 51*27*35*62*75 divided by 100

To find remainder when divided by 100:
Take ones place digit of each number: 1, 7, 5, 2, 5
Multiply them: 1 × 7 × 5 × 2 × 5 = 350
Find remainder when 350 ÷ 100 = 50 (remainder)

Therefore, when 51 × 27 × 35 × 62 × 75 is divided by 100, the remainder is 50.

Answer: (a) 50

Explanation :

Let’s solve this problem step by step:

Finding the least four-digit number with remainder 2 when divided by 3, 4, 5, and 6

STEP 1: Find the LCM of 3, 4, 5, and 6
– First, we need the least common multiple (LCM) of 3, 4, 5, and 6
– The LCM of these numbers is 60

STEP 2: Find the smallest four-digit number divisible by LCM
– We need to find the smallest four-digit number divisible by 60
– The smallest four-digit number divisible by 60 is 1020

STEP 3: Add remainder
– Since we want remainder 2 when divided by 3, 4, 5, and 6
– We add 2 to our number: 1020 + 2 = 1022

ANSWER: 1022 is the least four-digit number that leaves remainder 2 when divided by 3, 4, 5, and 6

VERIFICATION:
1022 ÷ 3 = 340 remainder 2
1022 ÷ 4 = 255 remainder 2
1022 ÷ 5 = 204 remainder 2
1022 ÷ 6 = 170 remainder 2

Explanation :

Recurring Decimal 1.272727…

To solve this problem, let x = 1.272727…

Then, 100x = 127.272727…

Subtracting x from 100x, we get:

• 99x = 126
• x = 126/99

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 3:

x = (126/3)/(99/3) = 42/33

We can simplify this fraction further by dividing the numerator and denominator by their greatest common factor, which is 3:

x = (42/3)/(33/3) = 14/11

Therefore, the recurring decimal representation 1.272727… is equivalent to 14/11, and the correct answer is (b).

Explanation :

For which period was the natural growth rate maximum ?

The natural growth rate is calculated by subtracting the death rate from the birth rate. From the data you provided, we can calculate the natural growth rates for each period:

• 1911-1921: 48.1 – 35.5 = 12.6
• 1921-1931: 46.4 – 36.3 = 10.1
• 1931-1941: 45.2 – 31.2 = 14
• 1941-1951: 39.9 – 27.4 = 12.5
• 1951-1961: 41.7 – 22.8 = 18.9
• 1961-1971: 41.1 – 18.9 = 22.2
• 1971-1981: 37.1 -14 .8 = 22.3

The maximum natural growth rate was 22.3 during the period 1971-1981.

Explanation : 

Largest Number

Let’s solve this problem step by step. A negative exponent means that the base is inverted and the exponent becomes positive. For example, (1/2)^-6 can be written as (2/1)^6.

Using this logic, we can rewrite all the options as follows:
(a) (1/2)^-6 = (2/1)^6 = 64
(b) (1/4)^-3 = (4/1)^3 = 64
(c) (1/3)^-4 = (3/1)^4 = 81
(d) (1/6)^-2 = (6/1)^2 = 36

So among these options, the largest number is 81.

So (c) (1/3)^-4 is indeed the correct answer.

Explanation :

A shop owner offers the following …

Let’s calculate the effective discount for each option, assuming the original price of the article is P.

Option 1:

First discount: 10% -> P * (1 – 0.10) = 0.9P
Second discount: 20% -> 0.9P * (1 – 0.20) = 0.9P * 0.8 = 0.72P
Service tax: 10% -> 0.72P * (1 + 0.10) = 0.72P * 1.1 = 0.792P

Option 2:

First discount: 20% -> P * (1 – 0.20) = 0.8P
Second discount: 10% -> 0.8P * (1 – 0.10) = 0.8P * 0.9 = 0.72P
Service tax: 10% -> 0.72P * (1 + 0.10) = 0.72P * 1.1 = 0.792P

Option 3:

Service tax: 10% -> P * (1 + 0.10) = 1.1P
First discount: 20% -> 1.1P * (1 – 0.20) = 1.1P * 0.8 = 0.88P
Second discount: 10% -> 0.88P * (1 – 0.10) = 0.88P * 0.9 = 0.792P

All three options result in the customer paying the same final price, which is 79.2% of the original price (0.792P). So, all options are equivalent in terms of the final price for the customer.