The value of x in the equation 3x-5 =10 is?
A. 3
B. 5
C. 7
D. 8
Answer
Correct Answer: B. 5
Detail about MCQs
Add 5 both sides
Simplify 10 + 5 to 15
3x = 15
Divide both sides by 3
X = 15/3
Simplify 15/3 to 5
X =5
Find the value of x in the inequality 3x-5>7
A. X>4
B. X<4
C. X>3
D. X<3
Answer
Correct Answer: A. X>4
Detail about MCQs
Solution: 3x−5>7
Eliminate the constant term −5
To simplify, add 5 to both sides of the inequality. This removes −5 from the left-hand side:
3x −5 +5 >7 +5
3x >12
: Isolate xxx
Now, divide both sides of the inequality by 3to solve for x. Since we are dividing by a positive number, the direction of the inequality remains unchanged
x> 12/3
x>4
If the arithmetic mean of seventy five numbers is 35. If each number is increased by 5, then mean of new number is ____?
A. 30
B. 40
C. 70
D. 90
Answer
Correct Answer: B. 40
Detail about MCQs
To find the new mean after increasing each number by 5, you can follow these steps:
1. Original mean: 35
2. Number of values: 75
When each number is increased by 5, the new mean will be:
New Mean=Original Mean+5
New Mean=35+5=40
So the correct answer is B. 40.
If 20% of an electricity bill is deducted, then Rs. 100 is till to be paid. How much was the original bill?
A. Rs. 115
B. Rs. 110
C. Rs. 125
D. None of these
Answer
Correct Answer: C. Rs. 125
Detail about MCQs
To solve this problem, let’s denote the original electricity bill amount as .
If 20% of the bill is deducted, the remaining amount to be paid is 100. This means 80% of the bill remains.
We can set up the equation as follows:
0.80×x=100
Now, let’s solve for :
x=100/0.80=125
So, the original electricity bill was Rs. 125.
Therefore, the correct answer is C. Rs. 125.
A shopkeeper earns 15% profit on a shirt even after allowing 31% discount on the list price. If list price is Rs125, then cost price of shirt is?
A. 87
B. 80
C. 75
D. None of these
Answer
Correct Answer: C. 75
Detail about MCQs
Let’s break down the problem step by step:
- The shopkeeper earns a 15% profit on the shirt.
- The shopkeeper offers a 31% discount on the list price.
First, let’s find out the selling price (SP) after applying the discount: Discount = 31% of the list price = 0.31 * 125 = Rs 38.75 So, the selling price after the discount = List price – Discount = Rs 125 – Rs 38.75 = Rs 86.25
Now, we know that the shopkeeper earns a 15% profit on the selling price. Let’s represent the cost price (CP) as x.
The selling price (SP) after profit = Cost price (CP) + Profit So, SP = CP + 15% of CP = CP + 0.15 * CP = 1.15 * CP
Given that SP = Rs 86.25, we can write the equation as: 1.15 * CP = 86.25
Now, we can solve for the cost price (CP): CP = 86.25 / 1.15 = Rs 75
So, the cost price of the shirt is Rs 75.
Therefore, the correct answer is C. 75.
How many numbers up to 450 are divisible by 4, 6 and 8 together?
A. 19
B. 18
C. 17
D. None of these
Answer
Correct Answer: B. 18
Detail about MCQs
To find the numbers up to 450 that are divisible by 4, 6, and 8 together, we need to find the numbers that are divisible by the least common multiple (LCM) of 4, 6, and 8.
The LCM of 4, 6, and 8 is the smallest number that is divisible by all three numbers, which can be found by calculating the prime factorization of each number:
- 4 = 2^2
- 6 = 2 * 3
- 8 = 2^3
To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3 = 24.
So, any number that is divisible by 24 is also divisible by 4, 6, and 8.
Now, to find how many numbers up to 450 are divisible by 24, we divide 450 by 24:
450 ÷ 24 = 18 with a remainder of 18.
So, there are 18 whole multiples of 24 up to 450.
Therefore, the correct answer is B. 18.
3 candidates participated in election and received 11628,1136 and 7636 votes. Calculate the percentage of the total votes that the winning candidate got ?
A. 70%
B. 59%
C. 57%
D. 62%
Answer
Correct Answer: C. 57%
Solution
The total number of votes cast in the election is:
11628 + 1136 + 7636 = 20400
Let’s call the winning candidate “A”, who received 11628 votes.
The percentage of the total votes that candidate A got is:
(11628/20400) x 100% ≈ 57.06%
Therefore, the answer is (C) 57%.
A number (85%) is added to 24, the answer is the same, Select that number from the list given below.
A. 190
B. 180
C. 170
D. 160
Answer
Correct Answer: D. 160
Solution
Let’s represent the unknown number as “x”.
According to the problem statement, adding 85% of “x” to 24 is the same as “x”. Mathematically, we can write this as:
x = x + 0.85x + 24
Simplifying the equation, we get:
0.15x = 24
x = 24/0.15 = 160
Therefore, the answer is (D) 160.
10 shoes are placed at somewhere in room. What is probability that a pair of shoes will always be together:
A. 8/10
B. 2/5
C. 1/5
D. 9/10
Answer
Correct Answer: B. 2/5
Solution
Let’s assume that the 10 shoes are distinguishable, i.e., we can tell them apart from one another.
We can arrange the 10 shoes in 10! (10 factorial) ways. However, for a pair of shoes to be together, we can treat the pair as a single entity, which means that we have 9 objects to arrange. We can arrange these 9 objects in 9! ways. Additionally, we can arrange the pair of shoes within themselves in 2! ways. Therefore, the total number of ways to arrange the 10 shoes such that the pair is together is:
9! × 2!
The total number of ways to arrange the 10 shoes without any restrictions is simply 10!.
Therefore, the probability that a pair of shoes will always be together is:
(9! × 2!) / 10!
Simplifying this expression, we get:
(9! × 2!) / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)
= 2 / 5
Therefore, the answer is option B – 2/5.
A number (60%) is added to 120, the answer is the same, Select the number from the options given below.
A. 400
B. 300
C. 250
D. 180
Answer
Correct Answer: B. 300
Solution
Let’s assume the number is x.
According to the problem, if we add 60% of x to 120, we get x again. This can be expressed as the following equation:
120 + 0.6x = x
Simplifying this equation, we get:
0.4x = 120
x = 120 / 0.4
x = 300
Therefore, the number is 300, and the answer is option B.