Maharashtra Board Class 6 Maths Chapter 11 Ratio Proportion Set 29 Solutions

Ratio-Proportion Class 6 Maths Chapter 11 Practice Set 29 Solutions Maharashtra Board

Std 6 Maths Practice Set 29 Solutions Answers

Question 1. If 20 metres of cloth costs Rs 3600, find the cost of 16 m of cloth.
Answer:
Solution:
Cost of 20 metres of cloth = Rs 3600
∴ Cost of 1 metre of cloth = \(\frac{\text{cost of 20 metres of cloth}}{20} = \frac{3600}{20}\)
= Rs 180
∴ Cost of 16 metres of cloth = Cost of 1 metre of a cloth × 16
= 180 x 16 = Rs 2880
∴ The cost of 16 metres of cloth is Rs 2880.
In simple words: To find the cost of 16m of cloth, first calculate the cost of 1m by dividing the total cost (Rs 3600) by the total length (20m). Then, multiply the cost of 1m (Rs 180) by 16 to get the cost of 16m.

🎯 Exam Tip: Clearly show the steps for calculating the unit cost first, as this is a fundamental concept in ratio and proportion problems and often carries partial marks.

Question 2. Find the cost of 8 kg of rice, if the cost of 10 kg is Rs 325.
Answer:
Solution:
Cost of 10 kg rice = Rs 325
∴ Cost of 1 kg rice
\(= \frac{\text{Cost of 10 kg rice}}{10} = \frac{325}{10} = \frac{325 \div 5}{10 \div 5} = \frac{65}{2}\)
Cost of 8 kg rice = Cost of 1 kg rice x 8
\(= \frac{65 \times 8}{2} = \frac{520}{2} = \text{Rs. } 260\)
∴ The cost of 8 kg rice is Rs 260.
In simple words: First, find the cost of 1 kg of rice by dividing the total cost (Rs 325) by the total quantity (10 kg). Then, multiply this unit cost (Rs 65/2) by 8 to find the cost of 8 kg of rice.

🎯 Exam Tip: Remember to simplify fractions where possible to make calculations easier, especially when dealing with division and multiplication in sequence.

Question 3. If 14 chairs cost Rs 5992, how much will have to be paid for 12 chairs?
Answer:
Solution:
Cost of 14 chairs = Rs 5992
∴ Cost of 1 chair
\(= \frac{\text{Cost of 14 chairs}}{14} = \frac{5992}{14}\)
= Rs 428
∴ Cost of 12 chairs = Cost of 1 chair x 12
= 428 x 12 = Rs 5136
∴ The amount to be paid for 12 chairs is Rs 5136.
In simple words: Determine the cost of a single chair by dividing the total cost (Rs 5992) by the number of chairs (14). Then, multiply this unit cost (Rs 428) by 12 to find the total cost for 12 chairs.

🎯 Exam Tip: Accuracy in division and multiplication is crucial. Double-check your calculations to avoid errors in multi-step problems.

Question 4. The weight of 30 boxes is 6 kg. What is the weight of 1080 such boxes?
Answer:
Solution:
Weight of 30 boxes = 6 kg
∴ Weight of 1 box
\(= \frac{\text{Weight of 30 boxes}}{30} = \frac{6}{30} = \frac{6 \div 6}{30 \div 6} = \frac{1}{5}\) kg
∴ Weight of 1080 boxes = Weight of 1 box x 1080
\(= \frac{1}{5} \times 1080 = \frac{1 \times 1080}{5 \times 1} = 216\) kg
∴ The weight of 1080 boxes is 216 kg.
In simple words: Calculate the weight of one box by dividing the total weight (6 kg) by the number of boxes (30). Then, multiply this unit weight (1/5 kg) by 1080 to find the total weight of 1080 boxes.

🎯 Exam Tip: When dealing with large numbers, simplifying the unit calculation early can prevent complex multiplications later on. Remember to include units in your final answer.

Question 5. A car travelling at a uniform speed covers a distance of 165 km in 3 hours. At that same speed,
a. How long will it take to cover a distance of 330 km?
b. How far will it travel in 8 hours?
Answer:
Solution:
Distance covered in 3 hours = 165 km
Distance covered in 1 hour
\(= \frac{\text{Distance covered in 3 hours}}{3} = \frac{165}{3}\)
= 55 km
a. Time required to cover a distance of 330 km
\(= \frac{\text{Total distance}}{\text{Distance covered in 1 hour}} = \frac{330}{55}\)
= 6 hours
∴ The time required to cover a distance of 330 km is 6 hours.
b. Distance traveled in 8 hours = Distance covered in 1 hour x 8
= 55 x 8 = 440 km
∴ The distance traveled in 8 hours is 440 km.
In simple words: First, find the car's speed by calculating the distance covered in one hour (165 km / 3 hours = 55 km/h). Then, for part (a), divide the new distance (330 km) by the speed to find the time. For part (b), multiply the speed by 8 hours to find the distance covered.

🎯 Exam Tip: Breaking down multi-part questions into individual calculations, such as finding the unit rate (speed), makes the problem-solving process clearer and easier to manage.

Question 6. A tractor uses up 12 litres of diesel while ploughing 3 acres of land. How much diesel will be needed to plough 19 acres of land?
Answer:
Solution:
Diesel required to plough 3 acres of land = 12 litres
∴ Diesel required to plough 1 acre of land
\(= \frac{\text{Diesel required to plough 3 acres of land}}{3} = \frac{12}{3}\)
= 4 liters
∴ Diesel required to plough 19 acres of land = Diesel required to plough 1 acre of land x 19
= 4 x 19 = 76 litres
∴ Diesel needed to plough 19 acres of land is 76 litres.
In simple words: Calculate the amount of diesel needed per acre by dividing the total diesel used (12 litres) by the area ploughed (3 acres). Then, multiply this per-acre requirement (4 litres/acre) by 19 to find the total diesel needed for 19 acres.

🎯 Exam Tip: Always identify the unit rate (diesel per acre, cost per kg, distance per hour) first in proportion problems. This simplifies subsequent calculations significantly.

Question 7. At a sugar factory, 5376 kg of sugar can be obtained from 48 tonnes of sugarcane. If Savitatai has grown 50 tonnes of sugarcanes, how much sugar will it yield?
Answer:
Solution:
Sugar obtained from 48 tonnes of sugarcane = 5376 kg
∴ Sugar obtained from 1 tonne of sugarcane
\(= \frac{\text{Sugar obtained from 48 tonnes of sugarcane}}{48}\)
\(= \frac{5376}{48} = \frac{5376 \div 16}{48 \div 16} = \frac{336}{3} = 112\) kg
∴ Sugar obtained from 50 tonnes of sugarcane = Sugar obtained from 1 tonne of sugarcane x 50
= 112 x 50 = 5600 kg
∴ 50 tonnes of sugarcane will yield 5600 kg of sugar.
In simple words: First, find out how much sugar is obtained from 1 tonne of sugarcane by dividing the total sugar (5376 kg) by the total sugarcane (48 tonnes). Then, multiply this per-tonne yield (112 kg/tonne) by 50 to find the total sugar from 50 tonnes of sugarcane.

🎯 Exam Tip: Pay attention to the units (kg vs. tonnes) in the problem, though here they are consistently used to derive the ratio, ensuring the final answer is in the correct unit (kg).

Question 8. In an orchard, there are 128 mango trees in 8 rows. If all the rows have an equal number of trees, how many trees would there be in 13 rows?
Answer:
Solution:
Number of mango trees in 8 rows = 128
Number of mango trees in 1 row
\(= \frac{\text{Number of mango trees in 8 rows}}{8} = \frac{128}{8}\)
= 16 trees
∴ Number of mango trees in 13 rows = Number of mango trees in 1 row x 13
= 16 x 13 = 208
∴ The number of mango trees in 13 rows are 208.
In simple words: Calculate the number of trees in one row by dividing the total trees (128) by the total rows (8). Then, multiply this per-row count (16 trees/row) by 13 to find the total number of trees in 13 rows.

🎯 Exam Tip: For problems involving equal distribution, finding the quantity per unit (like trees per row) is the key first step to solving for larger quantities.

Question 9. A pond in a field holds 120000 litres of water. It costs Rs 18000 to make such a pond. How many ponds will be required to store 480000 litres of water, and what would be the expense?
Answer:
Solution:
Capacity of 1 pond = 1,20,000 litres
Total quantity of water = 4,80,000 litres
∴ Number of ponds required
\(= \frac{\text{Total quantity of water}}{\text{Capacity of one pond}}\)
\(= \frac{4,80,000}{1,20,000} = \frac{4,80,000 \div 10,000}{1,20,000 \div 10,000} = \frac{48}{12} = 4\) ponds
Amount required to make 1 pond = Rs 18,000
∴ Amount required to make 4 ponds = Amount required to make 1 pond x 4
= 18,000 x 4 = Rs 72,000
∴ The number of ponds required to store 4,80,000 litres of water is 4, and the expense incurred in making the ponds is Rs 72,000.
In simple words: First, determine the number of ponds needed by dividing the total water to be stored (4,80,000 litres) by the capacity of one pond (1,20,000 litres). Then, calculate the total expense by multiplying the cost of one pond (Rs 18,000) by the number of ponds required.

🎯 Exam Tip: This problem involves two distinct calculations: finding the number of units (ponds) and then the total cost. Address each part systematically for full marks.

Maharashtra Board Class 6 Maths Chapter 11 Ratio-Proportion Practice Set 29 Intext Questions and Activities

Question 1. Vijaya wanted to gift pens to seven of her friends on her birthday. When she went to a shop to buy them, the shopkeeper told her the rate for a dozen pens. i. Can you help Vijaya to find the cost of 7 pens? ii. If you find the cost of one pen, you can also find the cost of 7, right? (Textbook pg. no. 59)
ℹ️ चित्र व्याख्या (Diagram Explanation): एक दुकान का दृश्य है जिसमें एक दुकानदार खड़ा है। एक लड़की (विजया) दुकानदार से 7 पेन खरीदने के लिए कहती है। दुकानदार ने डिस्प्ले पर 'एक दर्जन पेन की कीमत 84 रुपये' लिखी एक तख्ती दिखाई है।
Answer:
Solution:
Cost of 12 pens = Rs 84.
∴ Cost of 1 pen
\(= \frac{\text{Cost of 12 pens}}{12} = \frac{84}{12} = \text{Rs. } 7\)
∴ Cost of 7 pens = Cost of one pen x Number of pens = 7 x 7
∴ Cost of 7 pens = Rs 49
∴ The cost of 7 pens (Rs 49) can be found by unitary method.
In simple words: To find the cost of 7 pens, first calculate the cost of a single pen by dividing the price of a dozen (12) pens (Rs 84) by 12. Then, multiply the cost of one pen (Rs 7) by 7 to get the total cost for 7 pens.

🎯 Exam Tip: The unitary method (finding the cost/value of one unit first) is a versatile technique. Practice its application in various scenarios to master ratio-proportion problems.