The correct answer is (C) 6 litres of 50% and 4 litres of 25%

Explanation:

To solve this problem, we use the concept of mixture and alligation. Let’s break it down step by step:

Step 1: Define the variables
Let the amount of the 50% acid solution be x litres.
Then, the amount of the 25% acid solution will be (10 – x) litres, since the total mixture is 10 litres.

Step 2: Write the equation for the total acid content
The total acid content in the mixture is given by:
(Acid from 50% solution) + (Acid from 25% solution) = (Acid in 40% solution).

This can be written as:
0.50x + 0.25(10 – x) = 0.40(10)

Step 3: Simplify the equation
Expand and simplify:
0.50x + 2.5 – 0.25x = 4
0.25x + 2.5 = 4
0.25x = 4 – 2.5
0.25x = 1.5
x = 1.5 ÷ 0.25
x = 6

Step 4: Interpret the result
The amount of the 50% acid solution is 6 litres.
The amount of the 25% acid solution is 10 – 6 = 4 litres.

Final Answer: The correct option is (C) 6 litres of 50% and 4 litres of 25%.

The correct answer is (C) -19/11 < -8/5 < -3/2.

Explanation:

To solve this, we need to compare the given fractions: -8/5, -3/2, and -19/11. Since all the numbers are negative, the smaller the absolute value, the greater the number.

Step 1: Convert all fractions to decimals
-8/5 = -1.6
-3/2 = -1.5
-19/11 = -1.727 (approximately)

Step 2: Compare the decimals
From least to greatest:
The smallest number is -19/11 (-1.727).
The next smallest is -8/5 (-1.6).
The largest is -3/2 (-1.5).

Step 3: Write the order
From least to greatest: -19/11 < -8/5 < -3/2

Final Answer: The correct option is (C) -19/11 < -8/5 < -3/2.

The correct answer is (B) 14.

Explanation:

To solve this problem, let’s break it down step by step:

Step 1: Understand the given data
The probability of getting a bad egg is 0.035.
The total number of eggs in the lot is 400.

Step 2: Calculate the expected number of bad eggs
The expected number of bad eggs can be calculated as:
Number of bad eggs = Probability of a bad egg × Total number of eggs
Number of bad eggs = 0.035 × 400 = 14.

Final Answer: The correct option is (B) 14.

The correct answer is (C) 12 hours.

Explanation:

Step 1: Determine Sonia’s work rate
Sonia can copy 50 pages in 10 hours.
So, Sonia’s work rate is:
Work rate of Sonia = 50 pages ÷ 10 hours = 5 pages per hour.

Step 2: Determine the combined work rate of Sonia and Priya
Sonia and Priya together can copy 300 pages in 40 hours.
So, their combined work rate is:
Combined work rate = 300 pages ÷ 40 hours = 7.5 pages per hour.

Step 3: Determine Priya’s work rate
The combined work rate of Sonia and Priya is 7.5 pages per hour, and Sonia’s work rate is 5 pages per hour.
Thus, Priya’s work rate = Combined work rate – Sonia’s work rate = 7.5 – 5 = 2.5 pages per hour.

Step 4: Time taken by Priya to copy 30 pages
If Priya’s work rate is 2.5 pages per hour, the time taken by Priya to copy 30 pages is:
Time = Work ÷ Work rate = 30 ÷ 2.5 = 12 hours.

Final Answer: The correct option is (C) 12 hours.

The correct answer is (D) 2 days.

Explanation:

Step 1: Determine A’s work rate
A can complete 3/4 of the work in 12 days.
So, the amount of work A does in 1 day is:
Work rate = (3/4) ÷ 12 = (3/4) × (1/12) = 1/16 of the work per day.

Step 2: Time to complete 1/8 of the work
Now, we need to find how many days A will take to complete 1/8 of the work.
If A completes 1/16 of the work in 1 day, then the time required to complete 1/8 of the work is:
Time = (Work) ÷ (Work rate) = (1/8) ÷ (1/16) = 2 days.

Final Answer: The correct option is (D) 2 days.

The correct answer is (A) 16065

Explanation:

To determine the next number in the sequence 17, 17, 51, 255, 1785, let’s analyze the pattern:

1. First to Second Term: 17 to 17 is multiplied by 1.
2. Second to Third Term: 17 × 3 = 51.
3. Third to Fourth Term: 51 × 5 = 255.
4. Fourth to Fifth Term: 255 × 7 = 1785.

Observing the pattern, the multipliers are consecutive odd numbers: 1, 3, 5, 7. Following this pattern, the next multiplier should be 9.

5. Fifth to Sixth Term: 1785 × 9 = 16065.

The correct answer is (B) 20

Explanation:

Let’s solve this step by step.

1. First, let’s calculate the total cost for the peon:
Purchase price = ₹ 700
Repair cost = ₹ 170
Cartage cost = ₹ 30
Total cost = 700 + 170 + 30 = ₹ 900

2. Selling price = ₹ 1,080

3. To find gain percent:
Gain = Selling price – Cost price
Gain = 1,080 – 900 = ₹ 180

4. Gain percent = (Gain ÷ Cost price) × 100
= (180 ÷ 900) × 100
= 0.2 × 100
= 20%

Therefore, the gain percent is 20%. The answer is (B) 20.

The correct answer is (C) 55

Explanation:

Let’s solve this step by step.

1) Let’s say the two numbers are x and y

2) Given information:
x² + y² = 146
(x – y)² = 36

3) From (x – y)² = 36:
x² + y² – 2xy = 36

4) From x² + y² = 146:
Substituting this in the above equation
146 – 2xy = 36
-2xy = 36 – 146
-2xy = -110
xy = 55

5) Therefore, the product of both numbers is 55, (C) 55 is the correct answer.

The correct answer is (C) 5000%

Explanation:

Let’s solve this step by step:

1) When dividing percentages, we can treat them as regular numbers:
250% ÷ 5% = 2.5 ÷ 0.05

2) To divide by a decimal, we can multiply by its reciprocal:
2.5 ÷ 0.05 = 2.5 × (1/0.05) = 2.5 × 20 = 50

3) Since we’re dividing percentages, our answer should be in percentage form:
50 = 5000%

Therefore, the answer is (C) 5000%

The correct answer is (C) ₹5,000

Explanation:

Let’s solve this step by step.

1) Let’s say the amount invested at 8% is x
Then amount invested at 6% = (10,000 – x)

2) Given that total interest = ₹700
Interest from 8% investment = 8% of x = 0.08x
Interest from 6% investment = 6% of (10,000 – x) = 0.06(10,000 – x)

3) We can write the equation:
0.08x + 0.06(10,000 – x) = 700

4) Simplify right side of equation:
0.08x + 600 – 0.06x = 700

5) Combine like terms:
0.02x + 600 = 700
0.02x = 100
x = 5,000

6) Verification:
Amount at 8%: ₹5,000 → Interest = ₹400
Amount at 6%: ₹5,000 → Interest = ₹300
Total interest = ₹700 ✓

Therefore, the amount invested at 8% is ₹5,000.

The answer is (C) ₹5,000.