How Quantities Combine: Understanding Data

An assembly line worker produces $100$ units per hour during their regular $8$-hour shift. During $2$ hours of overtime, they produce $150$ units per hour. What is their average production rate per hour over the full $10$ hours?

A shop inventory includes $5$ watches with an average price of Rs $2000$ and $15$ clocks with an average price of Rs $400$. What is the average price of an item in this inventory?

A student mixes $1$ L of a $5\%$ sugar solution with $9$ L of pure water ($0\%$ sugar). What is the sugar concentration of the resulting $10$ L mixture?

Section A has $10$ students who read an average of $5$ books over the summer. Section B has $10$ students who read an average of $15$ books. What is the combined average number of books read per student?

A nutritionist is creating a health drink by mixing two types of fruit pulps. The details of the pulps used are given in the table below:

What is the average Vitamin C content (in mg per 100g) of the final $500$ g mixture?

A small construction team consists of 4 lead engineers who earn an average of Rs 80,000 per month and 6 junior technicians who earn an average of Rs 35,000 per month. What is the combined mean monthly salary of all 10 members of the team?

A logistics company fleet has two types of vans. Type 1 (40 vans) gets $12\text{ km/L}$ and Type 2 (10 vans) gets $18\text{ km/L}$. If each van travels the same distance, what is the combined average fuel efficiency for the whole fleet?

Three different metal alloys are melted together to form a new compound. Alloy A weighs $10$ kg and contains $40\%$ silver and $60\%$ copper. Alloy B weighs $20$ kg and contains $70\%$ silver and $30\%$ copper. Alloy C weighs $20$ kg and contains $25\%$ silver and $75\%$ copper. What is the ratio of silver to copper in the final $50$ kg compound?

A factory employs a certain number of workers. $60\%$ of the workers belong to the junior grade and earn an average daily wage of Rs $500$. The remaining workers are in the senior grade and earn an average of Rs $800$. After a policy change, $20$ junior workers are promoted to the senior grade (retaining their new senior wage of Rs $800$). If the new overall average daily wage of the factory becomes Rs $650$, how many workers are employed at the factory in total?

A quality control batch consists of $50$ type-A components with an average weight of $10$ g and $n$ type-B components with an average weight of $15$ g. If $10$ type-A components are removed and replaced by $10$ additional type-B components, the average weight of the entire batch increases by $0.5$ g. Find the total number of type-B components ($n$) originally present in the batch.

A coffee blend is made by mixing $300$ g of beans costing Rs $2$ per gram with $700$ g of beans costing Rs $1$ per gram. What is the average cost per gram of the blend?

A software tester finds an average of $3$ bugs per day during the first $5$ days of a project and an average of $8$ bugs per day during the next $5$ days. What is the combined average bugs found per day?

A group of $4$ seniors have an average age of $18$ years. A group of $6$ juniors have an average age of $13$ years. What is the sum of the ages of all $10$ students?

The table below shows the distribution of coins in two jars. Find the combined average value of a coin across both jars.

A community center runs two types of art workshops. The table below shows the number of participants and the average material fee paid per participant for each workshop type. What is the combined average material fee per participant for all the participants?

An investor has two accounts. Account A has Rs $20,000$ with an annual return of $12\%$. Account B has Rs $30,000$ with an annual return of $8\%$. What is the weighted average annual return for the total investment?

A company produces light bulbs in two batches. Batch 1 ($4000$ bulbs) has $2\%$ defects. Batch 2 ($6000$ bulbs) has $5\%$ defects. What is the overall percentage of defective bulbs across both batches?

A software team consists of $3$ Junior developers (average salary Rs $40,000$), $5$ Senior developers (average salary Rs $85,000$), and $2$ Managers. If the combined average salary for the whole $10$-member team is Rs $80,500$, what is the average salary of the two managers?

A library contains $5000$ books. $40\%$ of the books are Fiction with an average of $280$ pages. $35\%$ are Non-Fiction with an average of $320$ pages. The remaining $25\%$ are Reference books with an average of $500$ pages. What is the weighted average number of pages per book in the library?

A car travels from City A to City B in three stages. Stage 1 is $120$ km at an average speed of $40$ km/h. Stage 2 is $180$ km at $60$ km/h. Stage 3 is $100$ km at $50$ km/h. What is the average speed for the entire $400$ km journey?

Two equal quantities of juice are mixed. Batch A has $14\%$ sugar and Batch B has $22\%$ sugar. What is the resulting sugar percentage?

A $1\text{ litre}$ solution of $8\%$ salt is mixed with $3\text{ litres}$ of $12\%$ salt solution. Find the final concentration.

An alloy contains $300\text{ g}$ of copper at $60\%$ purity and $700\text{ g}$ of copper at $90\%$ purity. Find the final purity percentage of the copper alloy.

A tea blender mixes $10\text{ kg}$ of tea costing Rs $400/\text{kg}$ with $10\text{ kg}$ of tea costing Rs $600/\text{kg}$. What is the average cost of the mixture per kg?

A chef is preparing a large pot of specialty soup. He starts with $2\text{ litres}$ of base soup containing $1.5\%$ salt. To adjust the flavor, he adds $0.5\text{ litres}$ of concentrated broth containing $4\%$ salt and $2.5\text{ litres}$ of pure distilled water (containing $0\%$ salt). What is the final concentration of salt in the $5$-litre soup pot?

A jeweler combines three small batches of silver alloy to create a larger piece for a customized ornament. The details of the batches are as follows:

• Batch A: $40\text{ g}$ with $85\%$ purity
• Batch B: $60\text{ g}$ with $95\%$ purity
• Batch C: $100\text{ g}$ with $70\%$ purity

What is the overall silver purity percentage of the combined $200\text{ g}$ piece?

A technician is digging a narrow trench to lay water pipes. The trench is divided into three segments with different lengths and depths as shown in the table below. Following the weighted average method used in the Brāhmasphuṭasiddhānta, find the mean depth of the entire trench.

A jeweler melts a $120\text{ gram}$ gold ornament with a purity of $10\text{ Varna}$. He wishes to increase the purity of the gold to $13\text{ Varna}$ by adding a specific amount of pure gold ($16\text{ Varna}$). After the pure gold is added, what will be the total weight of the new gold alloy?

A metallurgy lab is preparing a new type of bronze. They combine $40\text{ kg}$ of an alloy that is $80\%$ copper and $20\%$ tin with $60\text{ kg}$ of a second alloy that is $70\%$ copper and $30\%$ tin. If $10\text{ kg}$ of pure copper is then added to this $100\text{ kg}$ mixture, what is the final percentage of tin in the resulting $110\text{ kg}$ alloy? (Round your answer to the nearest two decimal places).

A chemist needs to create $1.5\text{ litres}$ of a $32\%$ acid solution for an experiment. She has two stock bottles: one containing a $20\%$ acid solution and another containing an $80\%$ acid solution. How many millilitres of the $80\%$ acid solution must she mix with the $20\%$ solution to achieve her target concentration?

If a dataset has two scores, $10$ and $20$, and the weighted average is $18$, find the ratio of the weights $w_1:w_2$ for these scores.

A stock portfolio has two investments with weights $0.25$ and $0.75$. If the returns were $12\%$ and $4\%$ respectively, find the weighted average return.

A student’s overall grade is determined by Practical (weight $30\%$) and Theory (weight $70\%$). If the student scores $100$ in Practical and $60$ in Theory, calculate the total percentage.

A reviewer gives a restaurant $5$ stars for Food and $2$ stars for Ambience. If Food is $4$ times more important than Ambience, what is the weighted average rating?

A digital marketing firm evaluates the engagement of a post using a weighted score. The ratings for Likes, Comments, and Shares are on a $10$-point scale. Based on the importance levels provided in the table below, calculate the final weighted average engagement score.

A science project evaluation is based on three components: Research, Presentation, and Q&A. The weights assigned to these are in the ratio $2:3:1$. A student scored $15, 12,$ and $18$ respectively for these components, where each component was out of $20$. Find the student's overall weighted percentage score.

A smartphone's durability index is determined by weighting Material Strength, Water Resistance, and Screen Toughness in the ratio $3:4:3$. If a phone is rated $8, 6,$ and $10$ respectively for these categories on a $10$-point scale, calculate its overall weighted durability index.

A university grade is determined by weighting three independent components $X$, $Y$, and $Z$. Component $X$ is assigned a weight of $0.4$, while components $Y$ and $Z$ share the remaining weight. If a student's scores for $Y$ and $Z$ are equal, and they achieve a final weighted score of $82$ with a score of $70$ in component $X$, what was the student's score in component $Y$?

A customer support representative's performance score is calculated from their Resolution Rate ($R$), Response Time ($T$), and Customer Satisfaction ($S$). The weight of $S$ is $x\%$, and the remaining weight is shared equally between $R$ and $T$. A representative scores $80$ in $R$, $90$ in $T$, and $70$ in $S$. If their overall weighted average score is $76$, find the value of $x$.

An environmental project is evaluated based on its Carbon Footprint ($C$), Water Usage ($W$), and Land Degradation ($L$). The weights for these categories are determined by their respective environmental cleanup costs per unit: Rs $500$ for $C$, Rs $200$ for $W$, and Rs $300$ for $L$. Calculate the weighted average impact score for a project that has scores of $C=40$, $W=100$, and $L=60$.

In the provided geometry scene, if the circle represents total production (3600 units), how many units does the $60^\circ$ sector represent?

If the mean of 10 observations is 20, and each observation is multiplied by 3, what is the new mean?

Identify the mode from the following frequency table visualized as dots.

A circle graph (pie chart) shows that $25\%$ of a budget is spent on Rent. What is the central angle of the 'Rent' sector?

In a frequency distribution, the sum of frequencies is 100. If the relative frequency of a class is 0.15, what is its actual frequency?

What is the lower limit of the class interval $20 - 30$ in an inclusive distribution system if it was converted from $19.5 - 29.5$?

The following graph shows a data trend. If the trend continues linearly, what is the predicted value at $x = 6$?

A frequency distribution table is visualized as a set of concentric circles where the area of the ring (annulus) represents the frequency. If the inner radius is $5$ cm and the outer radius is $10$ cm for a specific class, and the total area of all classes is $400\pi$, what percentage of the total data does this class represent?

The following diagram shows a rectangular region with two quarter-circle corners removed for a garden design. If the rectangle is $20$ m by $12$ m and the radius of each quarter-circle is $4$ m, what is the area of the remaining region? (Use $\pi = 3.14$)

A data analyst is using a parabola $y = x^2 - 4x + 4$ to model the cost variation. At what value of $x$ is the cost minimum, and what is the minimum cost based on the visual interpretation of the vertex?

A savings chart shows contributions from 'Self' and 'Employer'. If 'Self' contributes $Rs\ 4000$ and 'Employer' contributes $Rs\ 2000$, identify the total height of the stacked bar.

A tower is built with two types of blocks: Red (bottom) and Blue (top). If the Red block is $15$ units high and the total tower height is $40$ units, what is the height of the Blue block?

In a stacked column chart representing $24$ hours of a day, the Sleep segment is $8$ hours and the School segment is $6$ hours. If these are the only two segments shown so far from the bottom, what is the $y$-coordinate of the top of the School segment?

A container holds two liquids, A and B, that do not mix. Liquid A (bottom) has a depth of $12$ cm and Liquid B (top) has a depth of $8$ cm. If these are represented in a stacked column, what is the value at the top boundary of Liquid B?

A stacked column of total height $H$ consists of four equal segments. If the third segment from the bottom is removed, what is the new total height?

A $200$ ml mixture has milk and water in the ratio $3:2$. If milk is the bottom segment and water is the top segment in a stacked column, what are the heights of the two segments?

Two years of data are shown. In Year 1, Segment A (bottom) is $50$ and Segment B (top) is $50$. In Year 2, Segment A increases by $10\%$ and Segment B decreases by $10\%$. What is the change in the total height of the stacked column?

Two local libraries, Alpha and Beta, display the composition of their book collections using 100% stacked bar charts. Based on the table below, which library has more absolute 'Reference' books and by what amount?

A bakery tracks its production costs using a stacked column consisting of Ingredients (bottom), Labor (middle), and Overheads (top). Initially, the total cost is Rs 1000, and the costs are distributed in the ratio $5:3:2$ respectively. Due to market changes, Labor costs rise by 50% and Ingredients costs drop by 20%, while Overheads remain constant. Based on the new costs, at what vertical coordinate (in Rs) will the top of the 'Labor' segment be located in a stacked column chart?

A logistics company uses a stacked column to track the weights of its monthly shipments. In Month 1, a shipment consisted of 100 kg of electronics and 400 kg of furniture. In Month 2, the total weight of the shipment increased by 25%, while the weight of the electronics component remained exactly the same as in Month 1. If a 100% stacked bar chart is created for Month 2 with the 'Electronics' segment at the base and the 'Furniture' segment on top, what is the percentage height occupied by the Furniture segment?

In a multi-set bar graph, the height of Bar 1 is $x$ and Bar 2 is $2x$. If $x=15$, what is the combined height of both bars?

If two squares of area $16$ $cm^2$ and $9$ $cm^2$ are placed side-by-side to form a composite shape, what is the total area of the shape?

A line segment AB is divided into two parts by point C. If AC = 4 cm and CB = 6 cm, what is the length of AB?

A tank is being filled by two pipes. Pipe 1 fills 10 liters/min and Pipe 2 fills 15 liters/min. How many total liters are collected in 1 minute?

A 'Square Chart' is used to represent the composition of a household's waste. The large square represents the total waste of $100$ kg. It is divided into smaller regions. If the region for 'Plastic' is a square with a side length of $4$ units within a larger $10 \times 10$ grid, what percentage of the total waste is Plastic?

The following segmented bar chart compares the production of wheat and rice in two farms, Farm A and Farm B. In Farm A, the ratio of wheat to rice is $3:2$. If the total production in Farm A is $500$ kg, and the bar for Farm A is $10$ cm high, what is the height of the segment representing Rice in the bar for Farm A?

A student tracks their monthly expenditure using a horizontal stacked bar chart (component bar chart) as an alternative to a pie chart. The total monthly budget is Rs 20,000. If the 'Education' segment is represented by a section of length 48 units on a total bar length of 120 units, what is the actual amount spent on Education?

A residential complex sits on a square plot of land measuring $100 \text{ m} \times 100 \text{ m}$. The land usage is divided as follows: Buildings (4000 $\text{m}^2$), Parking (2500 $\text{m}^2$), and a Green Area (the remaining portion). If this data is represented as an alternative to a pie chart using a $10 \times 10$ square grid (where each cell represents 1% of the total area), how many cells in the grid should be shaded to represent the Green Area?

In 2023, a student's total screen time was 8 hours per day, with 25% of it spent on educational apps. In 2024, the student reduced the total screen time to 6 hours per day. However, a 100% stacked bar chart for 2024 shows that 'Educational Apps' now occupy 40% of the daily total. By how many minutes did the absolute daily time spent on educational apps change from 2023 to 2024?

A factory has two production lines, A and B. Line A produces 500 units per day with a 4% defective rate. Line B produces 1500 units per day with an 8% defective rate. If the total combined production is represented in a 100% stacked bar chart that has a total height of 25 cm, what is the height of the segment representing the 'Defective' units?