Initial salary = 100
After two successive increments, final salary = 187.5
First increment = x%
Second increment =2x%

Going from the options, x=25%

The question is "After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was"

Hence, the answer is '25'

Single digit numbers where none of the digits is repeated = 1 to 9
⇒ n(single digit numbers)= 9
Double digit numbers = AB (where A is any number from 1 to 9 and B is any number except A)
⇒ n(double digit numbers) = 9 × 9 = 81
Triple digit numbers = ABC (where A is any number from 1 to 4, B is anything except A and C is anything except A, B)
⇒ n(triple digit numbers) = 4 × 9 × 8 = 288
Total number of numbers = 288 + 81 + 9 = 378

Total land area =20+30=50 hectares
In the total land area
Wheat part =1120×50=552
Mustard part =920×50=452
In Vimal's land area
Mustard
Wheat part =58×30=754
Mustard part =38×30=454
So, the land area for Rajesh
Wheat part =552−754=354
Mustard part =452−454=454
Ratio, Wheat : Mustard =354:454=7:9

A necessary condition for the system to have no solution for (𝑥,𝑦), is
The condition is a1a2=b1b2≠c1c2
i.e., p3=−4k≠2a
For p3=−4k;pk+12=0
For −4k≠2a;−4a≠2k⇒2a+k≠0
For p3≠2a;pa−6≠0

The question is "For some constant real numbers p,k and a, consider the following system of linear equations in x and y :

A necessary condition for the system to have no solution for (x,y), is "

Hence, the answer is '2a+k≠0'

Put x=1/x,

Solving (1) & (2),
(1) ⇒

Subtracting, we get

So,

Now,

Sum of the roots =−b/a
Answer =−3

The question is "For any non-zero real number x, let f(x)+2f(1x)=3x. Then, the sum of all possible values of x for which f(x)=3, is"

Hence, the answer is '-3'

We are thinking about two scenarios where x≥y and x≥−y. When x≥y,

So, the possibilities are ( 1,1 ), ( 1,0 ) and ( 1,−1 )
When x=0,
The possibilities are (0,1) and (0,−1)
When x=−1
The possibilities are ( −1,1 ), ( −1,0 ) and ( −1,−1 )
So, the number of distinct integer solutions =8

The question is "The number of distinct integer solutions (x,y) of the equation |x+y|+|x−y|=2, is"

Hence, the answer is '8'

Question:
A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is ?

Solution:

Interior angle of a regular octagon = (n−2)/n × 180°
= (8−2)/8 × 180° = 135°

Area of square ACEG = a²

In △BAC, using cosine rule:
a² = b² + c² − 2bc·cosC
a² = 6² + 6² − 2(6)(6)cos135°
a² = 72 − (72 × −√2/2)
a² = 72 + 36√2
a² = 36(2 + √2)

Therefore, Area = 36(2 + √2)

Answer: 36(2 + √2)  

Initial quantity of water in the container =x
So, initial quantity of milk in the container =300−x
Part of mixture taken out =2x300
Part of mixture that is retained =1−2x300
So, part of milk that is retained =(300−x)(1−2x300)
Also, quantity of milk that is retained after the iteration =72% of 300=216
Then,

The total content itself 300 litre. So, x=420 is inadmissible.
Thus, amount of water that was initially poured = 30 litre

Let, CP=x
Then, MP = 1.2 x ;

Also,
Savings = Rs. 15
Savings with respect to percentage =10% of MP=0.12x
Thus, 0.12x=15

Hence,

The question is "Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is"

Hence, the answer is '10'

Choice B is the correct answer.