Let first number = p
and second number = q
According to the question,
p - q = 18 ................................(i)
and 3p - 4q = 18.....................(ii)

Correct Option: D

Let first number = p
and second number = q
According to the question,
p - q = 18 ................................(i)
and 3p - 4q = 18.....................(ii)
On multiplying Eq .(i) by 3 and subtracting Eq. (ii) from it,we get
3p - 3q = 54
3p - 4q = 18
q = 36
On putting the value of q in Eq, (i) we get
p = 18 + q
⇒ p = 18 + 36 = 54
∴ Required sum = p + q = 54 + 36 = 90

Let total number of sweets distributed on children's day = x
According to the question,
x/250 - x/300 = 1

Correct Option: C

Let total number of sweets distributed on children's day = x
According to the question,
x/250 - x/300 = 1
⇒ ( 6x - 5x )/1500 = 1
∴ x = 1500
∴ Required number of sweets distributed on children's day = 1500

Let number of students in examination halls P and Q is x and y, respectively

Then as per the first condition,
x - 10 = y + 10
⇒ x - y = 20 ..............(i)
As per the second condition,
⇒ x + 20 = 2( y - 20)
⇒ x - 2y = - 60 ...............(ii)

Correct Option: D

Let number of students in examination halls P and Q is x and y, respectively

Then as per the first condition,
x - 10 = y + 10
⇒ x - y = 20 ..............(i)
As per the second condition,
⇒ x + 20 = 2( y - 20)
⇒ x - 2y = - 60 ...............(ii)
On subtraction Eq. (ii) from Eq. (i), we get
- y + 2y = 20 + 60
⇒ y = 80
Putting the value of y Eq. (i) we get,
x - 80= 20 ⇒ x = 100
Hence, number of students in examination halls P and Q is 100 and 80, respectively.

Let the number be x.
44² < x < 45²
⇒ 1936 < x < 2025 ...(i)

From equation (i), the required number will be any number between 1936 and 2025. Since one part of the number is the square of 6 means one factor is 36.

∴ L, C, M of 36 and 5 = 180
∴ Number will be multiple of 180 i,e.,
180 x 11 = 1980 the only value which satisfies the equation (i).

Correct Option: C

Let the number be x.
44² < x < 45²
⇒ 1936 < x < 2025 ...(i)

From equation (i), the required number will be any number between 1936 and 2025. Since one part of the number is the square of 6 means one factor is 36.

∴ L, C, M of 36 and 5 = 180
∴ Number will be multiple of 180 i,e.,
180 x 11 = 1980 the only value which satisfies the equation (i).

Method 1
Let Ram spends p minute on each Mathematics question.
According to the question.
50xp + 100 x p/2 + 50 x p/2 = 3 x 60
Solve the equation.

Method 2
Let Ram spends a minute on each sciences and Gk questions.
According to the question,
50 x 2a + 150 x a = 3 x 60
Solve the equation.

Correct Option: B

Let Ram spends p minute on each Mathematics question.
According to the question.
50 x p + 100 x p/2 + 50 x p/2 = 3 x 60
p(50+ 50 + 25) = 180
⇒ p = 180/125
∴ Required time = 50 x 180/125
∴ Required time = 2 x 180/5
∴ Required time = 2 x 36 = 72 min

Method 2
Let Ram spends a minute on each sciences and Gk questions.
According to the question,
50 x 2a + 150 x a = 3 x 60
100a + 150a = 180
250a = 180
a = 180/250
So total time spend on Mathematics question = 2a x 50 question
So total time spend on Mathematics question = 2 x 50 x 180/250 = 72 minutes