Direct and Inverse Proportions (Direct Proportion) interactive ... - Free Printable

Problem: Solving the worksheet on Direct Proportions

We will solve each problem step by step using the concept of direct proportion. In direct proportion, if one quantity increases, the other quantity also increases in the same ratio, and vice versa.

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Problem 1:

Rohit bought 12 registers for Rs 156. Find the cost of 7 such registers.

#### Solution:
- Cost of 12 registers = Rs 156
- Cost of 1 register = \( \frac{156}{12} = 13 \) Rs
- Cost of 7 registers = \( 7 \times 13 = 91 \) Rs

Answer: ₹ 91

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Problem 2:

Anupama takes 125 minutes to walk a distance of 100 meters. What distance would she cover in 315 minutes?

#### Solution:
- Distance covered in 125 minutes = 100 meters
- Distance covered in 1 minute = \( \frac{100}{125} = 0.8 \) meters
- Distance covered in 315 minutes = \( 315 \times 0.8 = 252 \) meters

Answer: 252 m

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Problem 3:

If the cost of 93 meters of a certain kind of plastic sheet is Rs 1395, then what would it cost to buy 105 meters of such plastic sheet?

#### Solution:
- Cost of 93 meters = Rs 1395
- Cost of 1 meter = \( \frac{1395}{93} = 15 \) Rs
- Cost of 105 meters = \( 105 \times 15 = 1575 \) Rs

Answer: ₹ 1575

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Problem 4:

Suneeta types 1080 words in one hour. What is her GWAM (gross words a minute rate)?

#### Solution:
- Words typed in 1 hour (60 minutes) = 1080
- Words typed in 1 minute = \( \frac{1080}{60} = 18 \)

Answer: 18 words per minute

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Problem 5:

A car is traveling at a speed of 50 kmph. How much distance would it travel in 12 minutes?

#### Solution:
- Speed = 50 km/hour
- Time = 12 minutes = \( \frac{12}{60} = 0.2 \) hours
- Distance = Speed × Time = \( 50 \times 0.2 = 10 \) km

Answer: 10 km

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Problem 6:

68 boxes of certain commodity require a shelf length of 13.6 meters. How many boxes of the same commodity would occupy a shelf length of 20.4 meters?

#### Solution:
- Shelf length for 68 boxes = 13.6 meters
- Shelf length for 1 box = \( \frac{13.6}{68} = 0.2 \) meters
- Number of boxes for 20.4 meters = \( \frac{20.4}{0.2} = 102 \)

Answer: 102 boxes

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Problem 7:

The second-class railway fare for 240 km of journey is Rs 15.00. What would be the fare for a journey of 139.2 km?

#### Solution:
- Fare for 240 km = Rs 15
- Fare for 1 km = \( \frac{15}{240} = 0.0625 \) Rs
- Fare for 139.2 km = \( 139.2 \times 0.0625 = 8.7 \) Rs

Answer: ₹ 8.70

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Problem 8:

If the thickness of a pile of 12 cardboards is 35 mm, find the thickness of a pile of 294 cardboards.

#### Solution:
- Thickness of 12 cardboards = 35 mm
- Thickness of 1 cardboard = \( \frac{35}{12} \) mm
- Thickness of 294 cardboards = \( 294 \times \frac{35}{12} = 857.5 \) mm = 85.75 cm

Answer: 85.75 cm

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Problem 9:

The cost of 97 meters of cloth is Rs 242.50. What length of this can be purchased for Rs 302.50?

#### Solution:
- Cost of 97 meters = Rs 242.50
- Cost of 1 meter = \( \frac{242.50}{97} = 2.5 \) Rs
- Length of cloth that can be purchased for Rs 302.50 = \( \frac{302.50}{2.5} = 121 \) meters

Answer: 121 m

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Problem 10:

A worker is paid Rs 210 for 6 days of work. If his total income for the month is Rs 875, for how many days did he work?

#### Solution:
- Payment for 6 days = Rs 210
- Payment for 1 day = \( \frac{210}{6} = 35 \) Rs
- Total income for the month = Rs 875
- Number of days worked = \( \frac{875}{35} = 25 \) days

Answer: 25 days

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Final Answers:

1. ₹ 91
2. 252 m
3. ₹ 1575
4. 18 words per minute
5. 10 km
6. 102 boxes
7. ₹ 8.70
8. 85.75 cm
9. 121 m
10. 25 days

Boxed Final Answer:
\[
\boxed{91, 252, 1575, 18, 10, 102, 8.70, 85.75, 121, 25}
\]