GSEB Class 6 Maths Solutions Chapter 12 Ratio and Proportion Exercise 12.3

Question 1. If the cost of 7 m of cloth is Rs 294, find the cost of 5 m of cloth.
Answer:
Cost of 7 m of fabric = Rs 294
So, the cost of 1 m of fabric = \( \frac { Rs\ 294 }{ 7 } = Rs\ 42 \)
Cost of 5 m of fabric = \( Rs\ (42 \times 5) = Rs\ 210 \)
Thus, the total cost of 5 m of fabric is Rs 210.
In simple words: First, figure out how much one meter of cloth costs. Then, multiply that amount by 5 to get the cost for 5 meters of cloth.

Exam Tip: Always clearly show the calculation for the unit cost (cost per 1 meter) before calculating for the desired quantity. This step earns crucial marks.

Question 2. Ekta earns Rs 1500 in 10 days. How much will she earn in 30 days?
Answer:
Ekta's earnings in 10 days = Rs 1500
So, Ekta's earnings in 1 day = \( \frac{Rs\ 1500}{10} = Rs\ 150 \)
As a result, Ekta's earnings in 30 days = \( Rs\ (150 \times 30) = Rs\ 4500 \)
Thus, Ekta will earn Rs 4500 in 30 days.
In simple words: To find out how much Ekta earns in 30 days, first calculate her daily earning. Then, multiply that by 30.

Exam Tip: This is a direct proportion problem. Clearly show the calculation for the daily earning (unit rate) to ensure full marks.

Question 3. If 276 mm of rain falls in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.
Answer:
Measure of rainfall in 3 days = 276 mm
So, the measure of rainfall in 1 day = \( \frac { 276 }{ 3 } \text{ mm} = 92 \text{ mm} \)
Therefore, the measure of rainfall in 7 days = \( (92 \times 7) \text{ mm} = 644 \text{ mm} \)
Thus, 644 mm of rain will drop in 7 days (which is one week).
In simple words: Figure out how much rain falls in one day. Then, multiply that amount by seven to find the total rainfall in a week. Remember to convert mm to cm if the question asks for cm in the final answer (not required here).

Exam Tip: Be careful with units! Ensure you're converting between mm and cm if required, and always specify the units in your answer.

Question 4. The cost of 5 kg of wheat is Rs 30.50.
(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased for Rs 61?
Answer:
(a)
Cost of 5 kg of wheat = Rs 30.50
Cost of 1 kg of wheat = \( \frac { 30.50 }{ 5 } = Rs\ 6.10 \)
So, cost of 8 kg of wheat = \( Rs\ (6.10 \times 8) = Rs\ 48.80 \)
Thus, the total cost of 8 kg of wheat is Rs 48.80.
(b)
Quantity of wheat that can be purchased for Rs 6.10 = 1 kg
So, quantity of wheat that can be purchased for Rs 1 = \( \frac { 1 }{ 6.10 } \text{ kg} \)
As a result, quantity of wheat that can be purchased for Rs 61 = \( \frac { 1 }{ 6.10 } \times 61 \text{ kg} = 10 \text{ kg} \)
Thus, 10 kg of wheat can be purchased for Rs 61.
In simple words: For part (a), find the cost of 1 kg of wheat first, then multiply by 8. For part (b), find how much wheat you get for Rs 1, then multiply by Rs 61.

Exam Tip: Break down the problem into smaller parts. Calculate the unit cost (cost per kg) or unit quantity (kg per rupee) first, then use it to find the final answer for each sub-question.

Question 5. The temperature dropped 15 degrees Celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?
Answer:
Drop in temperature in one day = \( \frac { 15 }{ 30 } \text{ degree} = 0.5 \text{ degree} \)
So, the drop in temperature in 10 days = \( 10 \times 0.5 \text{ degrees} = 5 \text{ degrees} \)
Thus, a 5 degree temperature drop will occur in the next 10 days.
In simple words: Figure out how much the temperature drops each day. Then, multiply that daily drop by 10 to find the total drop over ten days.

Exam Tip: Calculate the daily rate of change first. This 'unit rate' approach is crucial for solving problems involving consistent rates over different time periods.

Question 6. Shaina pays Rs 7500 as rent for 3 months. How much does she have to pay for a whole year, if the rent per month remains the same?
Answer:
Rent for 3 months = Rs 7500
Rent for 1 month = \( \frac { Rs\ 7500 }{ 3 } = Rs\ 2500 \)
So, rent for a whole year (which means 12 months) = \( Rs\ (12 \times 2500) = Rs\ 30000 \)
Thus, Shaina will need to pay Rs 30,000 for a full year.
In simple words: First, find out how much Shaina pays for one month's rent. Then, multiply that amount by 12 because there are 12 months in a year.

Exam Tip: Remember there are 12 months in a year. Always convert the given period to a unit (like 1 month) before calculating for the target period (12 months).

Question 7. The cost of 4 dozen bananas is Rs 60. How many bananas can be purchased for Rs 12.50?
Answer:
Since, 1 dozen of bananas = 12 bananas
So, 4 dozen of bananas = \( (12 \times 4) \) bananas = 48 bananas
Now, the number of bananas that can be purchased for Rs 60 = 48
Number of bananas that can be purchased for Rs 1 = \( \frac { 48 }{ 60 } = \frac { 4 }{ 5 } \)
Thus, number of bananas that can be purchased for Rs 12.50 = \( \frac { 4 }{ 5 } \times 12.50 = 4 \times 2.50 = 10 \)
As a result, 10 bananas can be purchased for Rs 12.50.
In simple words: First, find the total number of bananas in 4 dozen. Then, figure out how many bananas you can buy for Rs 1. Finally, multiply that by Rs 12.50.

Exam Tip: Convert dozens to individual units (bananas in this case) at the start to simplify calculations. Work with a unit cost or quantity before scaling up.

Question 8. The weight of 72 books is 9 kg. What is the weight of 40 such books?
Answer:
Weight of 72 books = 9 kg
Weight of 1 book = \( \frac { 9 }{ 72 } \text{ kg} = \frac { 1 }{ 8 } \text{ kg} \)
So, weight of 40 books = \( 40 \times \frac { 1 }{ 8 } \text{ kg} = 5 \text{ kg} \)
Thus, the total weight of 40 books is 5 kg.
In simple words: Calculate the weight of one book first. Then, multiply that weight by 40 to find the total weight of 40 books.

Exam Tip: Always find the weight of a single item (unit weight) when solving such problems. This provides a clear path to calculate the weight of any number of items.

Question 9. A truck requires 108 liters of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?
Answer:
Quantity of diesel required for 594 km = 108 liters
Quantity of diesel required for 1 km = \( \frac { 108 }{ 594 } \text{ litre} = \frac { 2 }{ 11 } \text{ litres} \)
So, quantity of diesel required for 1650 km = \( \frac { 2 }{ 11 } \times 1650 \text{ litres} = 2 \times 150 \text{ litres} = 300 \text{ litres} \)
Thus, 300 liters of diesel will be required to cover 1650 km.
In simple words: First, find out how much diesel the truck uses for one kilometer. Then, multiply that amount by 1650 to get the total diesel needed for the longer distance.

Exam Tip: Simplify fractions like \( \frac{108}{594} \) to their lowest terms (e.g., \( \frac{2}{11} \)) to make further calculations easier and prevent errors.

Question 10. Raju purchases 10 pens for Rs 150 and Manish buys 7 pens for Rs 84. Can you say who got the pens cheaper?
Answer:
For Raju:
Cost of 10 pens = Rs 150
So, cost of 1 pen = \( \frac { Rs\ 150 }{ 10 } = Rs\ 15 \)
For Manish:
Cost of 7 pens = Rs 84
So, cost of 1 pen = \( \frac { Rs\ 84 }{ 7 } = Rs\ 12 \)
Since, Rs 12 is less than Rs 15
Thus, Manish obtained the pens at a lower price.
In simple words: Calculate the price of one pen for Raju and the price of one pen for Manish. The person who paid less for a single pen got them cheaper.

Exam Tip: To compare prices, always calculate the unit price (cost per item) for each person or option. This allows for a fair and accurate comparison.

Question 11. Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?
Answer:
For Anish:
Number of runs made in 6 overs = 42
So, number of runs made in 1 over = \( \frac { 42 }{ 6 } = 7 \)
Thus, Anish made 7 runs per over.
For Anup:
Number of runs made in 7 overs = 63
So, number of runs made in 1 over = \( \frac { 63 }{ 7 } = 9 \)
Thus, Anup made 9 runs per over.
Hence, Anup made more runs per over.
In simple words: Find out how many runs Anish made in each over, and then do the same for Anup. The one with the higher number of runs per over scored more efficiently.

Exam Tip: To compare performance rates, always calculate the 'unit rate' (runs per over in this case) for each individual. This method simplifies the comparison.