Maharashtra Board Class 7 Chapter 9 Set 38 Direct Proportion and Inverse Proportion Solutions

Question 1. Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?
Answer: Solution:
Let 6 workers take \( x \) days and 15 workers take \( y \) days to weed the field.
The number of workers and the time required to weed the field are in inverse proportion.
\( \therefore 6 \times x = 5 \times 12 \)
\( x = \frac{5 \times 12}{6} \)
\( \therefore x = 10 \) days
Also, \( 15 \times y = 5 \times 12 \)
\( \therefore y = \frac{5 \times 12}{15} \)
\( = 4 \) days
\( \therefore \) 6 workers will take 10 days and 15 workers will take 4 days to weed the field.
In simple words: This problem involves inverse proportion, meaning as the number of workers increases, the time taken to complete the work decreases. We calculated the days required for 6 and 15 workers respectively based on this principle.

🎯 Exam Tip: Remember to correctly identify if the relationship is direct or inverse proportion before setting up the equation. Clearly state the final answer for each part of the question.

Question 2. Mohanrao took 10 days to finish a book, reading 40 pages every day. How many pages must he read in a day to finish it in 8 days?
Answer: Solution:
Let Mohanrao read \( x \) pages every day to finish the book in 8 days.
The number of pages read per day and the days required to finish the book are in inverse proportion.
\( \therefore 8 \times x = 10 \times 40 \)
\( x = \frac{10 \times 40}{8} \)
\( = 50 \)
\( \therefore \) Mohanrao will have to read 50 pages every day to finish the book in 8 days.
In simple words: This is an inverse proportion problem. To finish the book in fewer days, Mohanrao must read more pages per day. We calculated the required pages per day to meet the 8-day deadline.

🎯 Exam Tip: Ensure your calculations are accurate when dealing with inverse proportion problems. Present the final answer clearly stating the number of pages required per day.

Question 3. Mary cycles at 6 km per hour. How long will she take to reach her Aunt's house which is 12 km away? If she cycles at a speed of 4 km/hr, how long would she take?
Answer: Solution:
Speed of the cycle = \( 6 \) km/hr
Distance travelled to reach her Aunt's house = \( 12 \) km
\( \therefore \) Time required \( = \frac{\text{Distance travelled}}{\text{Speed}} \)
\( = \frac{12}{6} \)
\( = 2 \) hours
Let the time required when the speed of the cycle is \( 4 \) km/hr be \( x \) hours.
The speed of the cycle and the time required to travel the same distance are in inverse proportion.
\( \therefore 4 \times x = 6 \times 2 \)
\( x = \frac{6 \times 2}{4} \)
\( = 3 \) hours
\( \therefore \) Mary will require \( 2 \) hours if she is cycling at \( 6 \) km/hr and \( 3 \) hours if she is cycling at \( 4 \) km/hr to reach her Aunt's house.
In simple words: This problem demonstrates how speed and time are inversely proportional when distance is constant. We first found the time taken at 6 km/hr, then used inverse proportion to find the time taken at 4 km/hr.

🎯 Exam Tip: Clearly show the steps for calculating time at each speed. Understanding the inverse relationship between speed and time for a fixed distance is key here.

Question 4. The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people?
Answer: Solution:
Let the stock of grain last for \( x \) days for 6000 people.
The number of people and the days for which stock will last are in inverse proportion.
\( \therefore 6000 \times x = 4000 \times 30 \)
\( x = \frac{4000 \times 30}{6000} \)
\( = 20 \)
\( \therefore \) The stock of grain will last for \( 20 \) days for \( 6000 \) people.
In simple words: This is an inverse proportion scenario: more people mean the grain stock will last for fewer days. We calculated the duration the grain would last for an increased number of people.

🎯 Exam Tip: Correctly setting up the inverse proportion equation is vital. Make sure to present the final answer stating the number of days the stock will last.

Maharashtra Board Class 7 Maths Chapter 9 Direct Proportion And Inverse Proportion Practice Set 38 Intext Questions And Activities

Question 1. Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion. (Textbook pg. no. 65 and 66)
(i) Each student paid Rs 60 for the expenses. As there were 45 students,___rupees were collected. Had there been 50 students,___rupees would have been collected. The number of students and money collected are in___proportion.
(ii) The sweets shop near the school gave 90 laddoos for the picnic. If 45 students go for the picnic, each will get___laddoos. If 30 students go for the picnic, each will get___laddoos. The number of students and that of laddoos each one gets are in___proportion.
(iii) The farm is 120 km away from the school. The bus went to the farm at a speed of 40 km per hour and took___hours. On the return trip, the speed was 60 km per hour. Therefore, it took___hours. The speed of the bus and the time it takes are in___proportion.
(iv) The farmer picked 180 bors from his trees. He gave them equally to 45 students. Each student got___bors. Had there been 60 students, each would have got___bors. The number of students and the number of bors each one gets are in___proportion.
Answer:
(i) As there were 45 students, Rs 2700 rupees were collected. Had there been 50 students, Rs 3000 rupees would have been collected. The number of students and money collected are in direct proportion.
(ii) If 45 students go for the picnic, each will get 2 laddoos. If 30 students go for the picnic, each will get 3 laddoos. The number of students and that of laddoos each one gets are in inverse proportion.
(iii) The bus went to the farm at a speed of 40 km per hour and took 3 hours. On the return trip, the speed was 60 km per hour. Therefore, it took 2 hours. The speed of the bus and the time it takes are in inverse proportion.
(iv) He gave them equally to 45 students. Each student got 4 bors. Had there been 60 students, each would have got 3 bors. The number of students and the number of bors each one gets are in inverse proportion.
In simple words: This question explores scenarios of direct and inverse proportion. Direct proportion means as one quantity increases, the other increases proportionally. Inverse proportion means as one quantity increases, the other decreases proportionally.

🎯 Exam Tip: Accurately identifying whether a relationship is direct or inverse proportion is crucial. Clearly state the calculated values and the type of proportion for each sub-part.