This problem involves calculating profit and discount percentages. We are given the profit percentage and the discount percentage, and we need to find the percentage by which the goods were marked above the cost price. We can assume a cost price (e.g., 100) to simplify calculations and then work backward from the profit to find the selling price, and then use the discount to find the marked price, finally determining the markup percentage.
Assume Cost Price (CP):
Let the Cost Price (\(\text{CP}\)) of the goods be \(\text{Rs. } 100\).
Calculate Selling Price (SP) using Profit:
The shopkeeper gained \(71\%\) profit. Profit is calculated on the Cost Price.
\[\text{Profit} = 71\% \text{ of CP} = \frac{71}{100} \times 100 = \text{Rs. } 71\]Selling Price (\(\text{SP}\)) is Cost Price + Profit.
\[\text{SP} = \text{CP} + \text{Profit} = 100 + 71 = \text{Rs. } 171\]Calculate Marked Price (MP) using Discount:
The goods were sold at a discount of \(10\%\). Discount is always calculated on the Marked Price (\(\text{MP}\)).
If there is a \(10\%\) discount, the Selling Price is \( (100 - 10)\% \) of the Marked Price, which is \(90\%\) of the Marked Price.
\[\text{SP} = 90\% \text{ of MP}\] \[171 = \frac{90}{100} \times \text{MP}\]Now, solve for \(\text{MP}\):
\[\text{MP} = \frac{171 \times 100}{90} = \frac{1710}{9} = \text{Rs. } 190\]Calculate the percentage X:
The shopkeeper marked his goods at \(X\%\) above their cost price. This means the Marked Price is \((100 + X)\%\) of the Cost Price.
We have \(\text{CP} = \text{Rs. } 100\) and \(\text{MP} = \text{Rs. } 190\).
The amount marked above CP is \(\text{MP} - \text{CP} = 190 - 100 = \text{Rs. } 90\).
The percentage \(X\) is this amount as a percentage of the Cost Price:
\[X = \frac{\text{Amount marked above CP}}{\text{CP}} \times 100\%\] \[X = \frac{90}{100} \times 100\% = 90\%\]So, the value of \(X\) is \(90\).
D) 90
While covering a distance of 54 km, a man noticed that after cycling for 1 hour 15 minutes, the distance covered by him was \( \frac{7}{9} \) of the remaining distance. What was his speed in km/hr?
The problem involves calculating the speed of a man cycling a certain distance. We are given the total distance, the time spent cycling, and a relationship between the distance covered and the remaining distance after that time. We will use these pieces of information to find the distance covered in the given time and then calculate the speed.
B) 18.9 km/hr is the calculated speed of the man.
The problem presents a series of three-letter combinations. We need to identify the pattern in the alphabetical positions of the letters within each combination and across the combinations to find the missing term.
The pattern for the first letter is a decrease by 2 (14 - 2 = 12, 12 - 2 = 10, 10 - 2 = 8). Following this pattern, the next first letter should be \(8 - 2 = 6\), which corresponds to F.
The pattern for the second letter is also a decrease by 2 (20 - 2 = 18, 18 - 2 = 16, 16 - 2 = 14). Following this pattern, the next second letter should be \(14 - 2 = 12\), which corresponds to L.
The pattern for the third letter is also a decrease by 2 (26 - 2 = 24, 24 - 2 = 22, 22 - 2 = 20). Following this pattern, the next third letter should be \(20 - 2 = 18\), which corresponds to R.
The first letter is F, the second letter is L, and the third letter is R. Combining these gives FLR.
Correct Option: C) FLR
The question asks to identify which of the given options is NOT an industrial corridor planned under the Government of India's infrastructure initiatives. This requires knowledge of the major industrial corridors being developed in India.
Correct Option: A) Kolkata-Lucknow Industrial Corridor
The Kolkata-Lucknow Industrial Corridor is not one of the officially planned and implemented industrial corridors under the Government of India's major infrastructure initiatives. While there are plans for various connectivity projects, a dedicated industrial corridor with this specific name and alignment is not among the established ones.
This problem involves logical deduction to determine the floor numbers of six people (A, B, C, D, E, F) living on six different floors. We need to use the given clues to assign each person to a unique floor from 1 to 6 and then calculate the sum of the floors for A and E.
The possible pairs of floor numbers (from 1 to 6) whose product is 15 are:
So, F and D must live on floors 3 and 5, but not necessarily in that order. This means either F is on floor 3 and D on floor 5, or F is on floor 5 and D on floor 3.
This means E and C occupy consecutive floors. Possible pairs \((C, E)\) are:
We know D is either on floor 3 or floor 5 (from clue 1).
If D is on floor 3, then \(A + 3 = 7\), which means \(A = 4\).
In this case, F must be on floor 5 (from clue 1, as D is on 3).
So far: D=3, A=4, F=5.
Now consider E and C (consecutive floors). The remaining floors are 1, 2, 6. The only consecutive pair from these is (1, 2). So, C=1, E=2.
This assignment is consistent: A=4, B=6, C=1, D=3, E=2, F=5. All floors (1-6) are occupied by different people.
If D is on floor 5, then \(A + 5 = 7\), which means \(A = 2\).
In this case, F must be on floor 3 (from clue 1, as D is on 5).
So far: D=5, A=2, F=3.
Now consider E and C (consecutive floors). The remaining floors are 1, 4, 6. There are no consecutive floors among these (1, 4, 6). This case is not possible.
The only valid arrangement is:
Sum \( = A + E = 4 + 2 = 6\).
A) 6 is the correct sum of floors for A and E.
To solve this problem, we need to apply the given operations to each digit of the original number based on whether it is odd or even. Then, we will form a new number and count how many digits appear more than once in this new number.
A) Two — The digits 2 and 4 each appear twice in the new number 6082442. Therefore, two digits appear more than once.
To find the maximum volume of each identical container, we need to find the largest number that can divide both 168 litres (Oil A) and 234 litres (Oil B) without leaving a remainder. This is equivalent to finding the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of 168 and 234.
Volume of Oil A = 168 litres
Volume of Oil B = 234 litres
Each container must have only one type of oil, all containers must be completely filled, and all oil must be poured into these containers. This means the volume of each container must be a common factor of both 168 and 234.
To find the maximum volume, we need to find the HCF of 168 and 234.
First, find the prime factors of 168:
\[ 168 = 2 \times 84 \]\[ 168 = 2 \times 2 \times 42 \]\[ 168 = 2 \times 2 \times 2 \times 21 \]\[ 168 = 2^3 \times 3 \times 7 \]Next, find the prime factors of 234:
\[ 234 = 2 \times 117 \]\[ 234 = 2 \times 3 \times 39 \]\[ 234 = 2 \times 3 \times 3 \times 13 \]\[ 234 = 2 \times 3^2 \times 13 \]Now, find the HCF by taking the common prime factors raised to the lowest power:
\[ \text{HCF}(168, 234) = 2^1 \times 3^1 \]\[ \text{HCF}(168, 234) = 2 \times 3 \]\[ \text{HCF}(168, 234) = 6 \]The maximum volume of each container is 6 litres.
B) 6 — The HCF of 168 and 234 is 6. This means that containers of 6 litres can perfectly hold all of Oil A (168 / 6 = 28 containers) and all of Oil B (234 / 6 = 39 containers) without any oil left over or any container partially filled. This is the largest possible volume for such containers.
The question asks to identify the type of farming practiced in hill regions where slopes are cut into steps. This technique is specifically designed to adapt agriculture to mountainous terrain and prevent soil erosion.
D) Terrace farming is a method of farming where steps known as terraces are built into the slopes of hills and mountains. This technique helps to reduce soil erosion, conserve water, and make cultivation possible on steep terrain by creating flat, arable land.
The length, width and height of a cuboid are in the ratio 10 : 17 : 14, and its total surface area is 1096 cm2. Find the length (in cm) of the cuboid.
To find the length of the cuboid, we will first use the given ratio of length, width, and height to express them in terms of a common variable. Then, we will use the formula for the total surface area of a cuboid and the given total surface area to solve for that variable. Finally, we will substitute the value of the variable back into the expression for the length.
Represent the dimensions:
Given that the length, width, and height of the cuboid are in the ratio \(10 : 17 : 14\), we can represent them as:
where \(x\) is a common multiplier.
Formula for Total Surface Area (TSA):
The formula for the total surface area of a cuboid is:
\[ \text{TSA} = 2(lw + wh + hl) \]Substitute and form the equation:
Substitute the expressions for \(l, w,\) and \(h\) into the TSA formula:
\[ \text{TSA} = 2((10x)(17x) + (17x)(14x) + (14x)(10x)) \]\[ \text{TSA} = 2(170x^2 + 238x^2 + 140x^2) \]\[ \text{TSA} = 2(548x^2) \]\[ \text{TSA} = 1096x^2 \]Solve for \(x\):
We are given that the total surface area is \(1096 \text{ cm}^2\). So, we set up the equation:
\[ 1096x^2 = 1096 \]\[ x^2 = \frac{1096}{1096} \]\[ x^2 = 1 \]\[ x = \sqrt{1} \]\[ x = 1 \quad (\text{since length cannot be negative}) \]Calculate the length:
Now, substitute the value of \(x\) back into the expression for the length:
\[ \text{Length} = 10x = 10(1) = 10 \text{ cm} \]Correct Option: B) 10
The length of the cuboid is \(10 \text{ cm}\).
The problem presents a series of letter-number clusters. We need to identify the pattern in the letters and numbers separately to find the next cluster in the series.
The next cluster in the series should be JM67.
Correct Option: C) JM67 is the cluster that logically completes the series, as derived from the patterns of decreasing letters and increasing numbers.