Explanation :

Article’s Final Price Calculations

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.

Explanation :

Car’s Cost Price

Let’s solve this problem step by step. The person sold the car for Rs. 3,00,000 and incurred a loss of 20%. This means that the selling price of the car is 80% of its cost price.

We can represent the cost price of the car as x. Since the selling price is 80% of the cost price, we can write an equation: 0.8x = 3,00,000.

Solving for x, we find that x = (3,00,000) / (0.8) = Rs. 3,75,000.

So (d) Rs. 3,75,000 is indeed the correct answer.

Explanation : 

Two metallic cubes P and Q

Since each side of cube Q is two times that of cube P, the volume of Q will be 2^3 = 8 times that of P. This means y = 8x. Since the mass of Q is two times that of P, we have n = 2m. Now we can use these relationships to find the relationship between u and v.

u = m/x and v = n/y

Substituting n = 2m and y = 8x into v = n/y

gives us: v = (2m)/(8x) v = m/(4x)

Since u=m/x, we can see that u=4v.

So the correct answer is (a) u=4v.

Explanation : 

The integers between 1 and 100 which have 4 as a digit are:

4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84 and 94
So, there are a total 19 such integers.
Out of these, the integers which are divisible by 4 are:
4, 24, 40, 44, 48, 64 and 84
So, the number of integers not divisible by 4 = 19 – 7 = 12 integers

Explanation : 

Overall Average marks in Hindi

Let’s assume that there are x girls and y boys in the class. From the given data we can write two equations:

The total marks in English for girls and boys combined is (9x + 8y), and the overall average marks in English is 8.8, so (9x + 8y)/(x+y) = 8.8.

The total marks in Hindi for girls and boys combined is (8x + 7y).
Solving equation (1) for x in terms of y, we get: x = 4y.

Substituting this value of x into the expression for total marks in Hindi, we get: (8(4y) + 7(y))/(4y+y) = (39y)/(5y) = 7.8.

So the overall average marks in Hindi is 7.8.

Explanation : 

A3BC + DE2F = 15902

As per the given condition in the question, each letter represents a different digit greater than 3.
So we can replace the letters with 4, 5, 6, 7, 8, or 9.
A3BC + DE2F = 15902
Step 1: Unit digit
If we add C & F, then we should get 12. Only then can we get 2 at the unit place in the sum (15902).
So, C, F can be (4, 8) or (5, 7)
Step 2: Tens digit
We got a carry of 1 from 12. Now, we know that the tens digit of the sum, 15902 is 0.
So, B + 2 = 9
Or B = 7
Hence, C, F cannot be (5, 7). They must be (4, 8).
Step 3: Hundreds digit
We got a carry of 1 from 10. Now, we know that the hundreds digit of the sum, 15902 is 9.
So, E + 3 = 8
Or E = 8 – 3 = 5
Hence, we found that B =7, C = 4/8, E = 5 and F = 4/8
So, A/D = 6/9
So, difference between A and D = 9 – 6 = 3

Explanation : 

Torn Pages Numbers

Let us assume that, the numbers written on the both sides of the missing page are x and (x + 1).
Since the sum of the numbers on the remaining pages is 195, we can set up the equation:

1 + 2 + 3 + … + (n-1) + n = 195 + x + (x+1)

We know that the sum of the first n natural numbers is:

1 + 2 + 3 + … + (n-1) + n = n(n+1)/2

Substituting this in our equation, we get:

• n(n+1)/2 = 195 + x + (x+1)
• n(n+1) = 2(195 + 2x + 1)
• n^2 + n = 2(2x + 196)
• n^2 + n = 4x + 392

Now we need to find which pair of consecutive numbers (x, x+1) will satisfy this equation. We can try each option:

For option (b) x = 7, n = 20, and this satisfies the equation.

Therefore, the torn page contains numbers 7 and 8, which is option (b).

Explanation : 

Next number in sequence

If we subtract 1 from each number in the original sequence, we get the following sequence:

13, 17, 19, 23, 29, 31

Notice that this is simply the sequence of prime numbers starting from 13.

The next prime number after 31 is 37. Therefore, the next number in the original sequence, which corresponds to the prime number 37 after subtracting 1, is:

37 + 1 = 38

Therefore, the correct answer is (c) 38

Explanation :

x+1x+5x+xx+x1=1xx

x + 1x + 5x + xx + x1 = 1xx

=> x + 10+ x + 50 + x +10x + x + 10x + 1 = 100 + 10x + x

=> 24x + 61 = 100 + 11x

=> 13x = 39

=> x = 3

Explanation : 

Five-digit prime numbers

To determine how many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4, and 5 without repetition, we can use the fact that a number is prime if and only if it is divisible only by 1 and itself.

Next, consider the sum of the digits of any five-digit number formed using these digits. The sum is 1 + 2 + 3 + 4 + 5 = 15, which is divisible by 3. Therefore, Zero is the answer.