Maharashtra Board Class 7 Chapter 9 Set 39 Direct Proportion and Inverse Proportion Solutions

Question 1. Suresh and Ramesh together invested Rs. 144000 in the ratio 4 : 5 and bought a plot of land. After some years they sold it at a profit of 20%. What is the profit each of them got?
Answer:
Total investment = Rs. 144000
Profit earned = 20%
\( \therefore \) Total profit = 20% of 144000 = \( \frac{20}{100} \times 144000 \) = Rs. 28800
Proportion of investment of Suresh and Ramesh = 4:5
Let the profit of Suresh be Rs. 4x and that of Ramesh be Rs. 5x.
4x + 5x = 28800
\( \therefore \) 9x = 28800
\( \implies x = \frac{28800}{9} \)
= 3200
\( \therefore \) Suresh’s profit = 4x = 4 \( \times \) 3200 = Rs. 12800
Ramesh’s profit = 5x = 5 \( \times \) 3200 = Rs. 16000
\( \therefore \) The profit earned by Suresh and Ramesh are Rs. 12800 and Rs. 16000 respectively.
In simple words: सुरेश और रमेश ने कुल ₹1,44,000 निवेश किए और 20% लाभ पर बेचा. उनके निवेश के अनुपात (4:5) के आधार पर, सुरेश को ₹12,800 और रमेश को ₹16,000 का लाभ हुआ।

🎯 Exam Tip: Always calculate the total profit first, then distribute it according to the given investment ratio. Showing intermediate steps for calculating 'x' is crucial.

Question 2. Virat and Samrat together invested Rs. 50000 and Rs. 120000 to start a business. They suffered a loss of 20%. How much loss did each of them incur?
Answer:
Total investment = Rs. 50000 + Rs. 120000 = Rs. 170000
Loss incurred = 20%
\( \therefore \) Total loss = 20% of 170000 = \( \frac{20}{100} \times 170000 \) = Rs. 34000
Proportion of investment = 50000 : 120000
= 5:12 (Dividing by 10000)
Let the loss incurred by Virat be Rs. 5x and that by Samrat be Rs. 12x.
5x + 12x = 34000
\( \therefore \) 17x = 34000
\( \implies x = \frac{34000}{17} \)
= 2000
\( \therefore \) Virat’s loss = 5x = 5 \( \times \) 2000 = Rs. 10000
Samrat’s loss = 12x = 12 \( \times \) 2000 = Rs. 24000
\( \therefore \) The loss incurred by Virat and Samrat are Rs. 10000 and Rs. 24000 respectively.
In simple words: विराट और सम्राट ने कुल ₹1,70,000 निवेश किए और 20% का नुकसान हुआ, यानी कुल ₹34,000 का नुकसान। उनके निवेश के अनुपात (5:12) के अनुसार, विराट को ₹10,000 और सम्राट को ₹24,000 का नुकसान हुआ।

🎯 Exam Tip: When dealing with losses, the process is similar to profits – first find the total loss amount, then distribute it based on the investment ratio. Be careful with calculations of 'x'.

Question 3. Shweta, Piyush and Nachiket together invested Rs. 80000 and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was Rs. 30000 and Piyush’s Rs. 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of the profit?
Answer: 
Total investment = Rs. 80000
Nachiket’s investment = Total investment - (Shweta’s investment + Piyush’s investment)
= 80000 - (30000+ 12000)
= 80000 - 42000 = Rs. 38000
Profit earned = 24%
\( \therefore \) Total profit = 24% of 80000 = \( \frac{24}{100} \times 80000 \) = Rs. 19200
Proportion of investment = 30000 : 12000 : 38000
= 15:6:19 (Dividing by 2000)
Let the profit of Shweta, Piyush and Nachiket be Rs. 15x, Rs. 6x and Rs. 19x respectively.
15x + 6x + 19x = 19200
\( \therefore \) 40x = 19200
\( \implies x = \frac{19200}{40} \)
= 480
\( \therefore \) Nachiket’s profit = 19x = 19 \( \times \) 480 = Rs. 9120
\( \therefore \) Nachiket’s investment is Rs. 38000 and his profit is Rs. 9120.
In simple words: श्वेता, पीयूष और नचिकेत ने ₹80,000 का कुल निवेश किया, जिसमें से नचिकेत का निवेश ₹38,000 था। 24% के कुल लाभ ₹19,200 में से, नचिकेत को उनके निवेश अनुपात के अनुसार ₹9,120 का लाभ मिला।

🎯 Exam Tip: First, determine the unknown investment (Nachiket's) by subtracting known investments from the total. Then, calculate the total profit and distribute it based on the derived investment ratio to find individual shares.

Question 4. A and B shared a profit of Rs. 24500 in the proportion 3 : 7. Each of them gave 2% of his share of the profit to the Soldiers' Welfare Fund. What was the actual amount given to the Fund by each of them?
Answer: 
Proportion of share = 3:7
Let the profits of A and B be Rs. 3x and Rs. 7x respectively.
3x + 7x = 24500
\( \therefore \) 10x = 24500
\( \implies x = \frac{24500}{10} \)
= 2450
Profit earned by A = 3x = 3 \( \times \) 2450 = Rs. 7350
Amount given by A = 2% of his profit
= \( \frac{2}{100} \times 7350 \) = Rs. 147
Profit earned by B = 7x = 7 \( \times \) 2450 = Rs. 17150
Amount given by B = 2% of his profit
= \( \frac{2}{100} \times 17150 \) = Rs. 343
\( \therefore \) The amount given by A and B to the Soldiers' Welfare Fund are Rs. 147 and Rs. 343 respectively.
In simple words: A और B ने ₹24,500 का लाभ 3:7 के अनुपात में साझा किया। A का लाभ ₹7,350 और B का लाभ ₹17,150 था। प्रत्येक ने अपने लाभ का 2% सैनिक कल्याण कोष में दिया, जिससे A ने ₹147 और B ने ₹343 का योगदान दिया।

🎯 Exam Tip: First, calculate each person's share of the total profit. Then, calculate the percentage contribution from each individual's profit to the fund. Ensure careful percentage calculations.

Question 5. Jaya, Seema, Nikhil and Neelesh put in altogether Rs. 360000 to form a partnership, with their investments being in the proportion 3 : 4 : 7 : 6. What was Jaya’s actual share in the capital? They made a profit of 12%. How much profit did Nikhil make?
Answer:
Total investment = Rs. 360000
Profit earned = 12%
\( \therefore \) Total profit = 12% of 360000
= \( \frac{12}{100} \times 360000 \) = Rs. 43200
Proportion of investment = 3:4:7:6
Let the investment of Jaya, Seema, Nikhil and Neelesh be Rs. 3x, Rs. 4x, Rs. 7x and Rs. 6x respectively.
3x + 4x + 7x + 6x = 360000
\( \therefore \) 20x = 360000
\( \implies x = \frac{360000}{20} \)
= 18000
\( \therefore \) Jaya’s investment = 3x = 3 \( \times \) 18000 = Rs. 54000
Also, profit made by them is Rs. 43200
\( \therefore \) 3x + 4x + 7x + 6x = 43200
\( \therefore \) 20x = 43200
\( \implies x = \frac{43200}{20} \)
= 2160
\( \therefore \) Nikhil’s profit = 7x = 7 \( \times \) 2160 = Rs. 15120
\( \therefore \) Jaya’s share in the capital was Rs. 54000 and the profit made by Nikhil was Rs. 15120.
In simple words: जया, सीमा, निखिल और नीलेश ने ₹3,60,000 का निवेश 3:4:7:6 के अनुपात में किया। जया का वास्तविक पूंजी में हिस्सा ₹54,000 था। उन्हें 12% का कुल लाभ हुआ, जिसमें से निखिल का लाभ ₹15,120 था।

🎯 Exam Tip: Remember to calculate 'x' separately for the investment amount and for the profit distribution, as the 'x' values will differ. Clearly state both Jaya's capital share and Nikhil's profit share as requested.

Maharashtra Board Class 7 Maths Chapter 9 Direct Proportion And Inverse Proportion Practice Set 39 Intext Questions And Activities

Question 1. Saritaben, Ayesha and Meenakshi started a business by investing Rs. 2400, Rs. 5200 and Rs. 3400. They made a profit of 50%. If they reinvested all their profit by adding it to the capital, find out the proportions of their shares in the capital during the following year. (Textbook pg. no. 67)
Answer: 
Total investment = Rs. 2400 + Rs. 5200 + Rs. 3400 = Rs. 11000
Total profit = 50% of 11000 = \( \frac{50}{100} \times 11000 \) = Rs. 5500
Proportion of shares = 2400 : 5200 : 3400
= 12:26:17 (Dividing by 200)
Let the profit of Saritaben, Ayesha and Meenakshi be Rs. 12x, Rs. 26x and Rs. 17x respectively.
12x + 26x + 17x = 5500
\( \therefore \) 55x = 5500
\( \implies x = 100 \)
\( \therefore \) Saritaben’s profit = 12x = 12 \( \times \) 100 = Rs. 1200
Ayesha’s profit = 26x = 26 \( \times \) 100 = Rs. 2600
Meenakshi’s profit = 17x = 17 \( \times \) 100 = Rs. 1700
\( \therefore \) Saritaben’s new investment = 2400 + 1200 = Rs. 3600
Ayesha’s new investment = 5200 + 2600 = Rs. 7800
Meenakshi’s new investment = 3400 + 1700 = Rs. 5100
\( \therefore \) New proportion of shares = 3600 : 7800 : 5100
= 12:26:17 (Dividing by 300)
\( \therefore \) The proportion of the shares in the capital during the following year is 12: 26:17
In simple words: सरिताबेन, आयशा और मीनाक्षी ने कुल ₹11,000 का निवेश करके व्यवसाय शुरू किया और 50% लाभ कमाया, यानी ₹5,500। उन्होंने अपना पूरा लाभ पुनः निवेश किया। अगले वर्ष के लिए, उनकी नई पूंजी का अनुपात 12:26:17 होगा।

🎯 Exam Tip: This question involves a two-step process: first calculate the current year's profit distribution, and then add these profits back to the original investments to find the new capital and its proportion for the next year. Always simplify ratios to their lowest terms.

Question 2. Are the amount of petrol filled in a motorcycle and the distance traveled by it, in direct proportion? (Textbook pg. no. 63)
Answer: 
Yes.
If amount of petrol filled in the motorcycle is less, it will travel less distance and if the amount of petrol filled is more, it will travel more distance.
Hence, the amount of petrol filled in the motorcycle and the distance traveled by it are in direct proportion.
In simple words: हां, मोटरसाइकिल में भरे पेट्रोल की मात्रा और उसके द्वारा तय की गई दूरी सीधे समानुपात में होती हैं क्योंकि अधिक पेट्रोल से अधिक दूरी तय की जा सकती है।

🎯 Exam Tip: Direct proportion means that as one quantity increases, the other quantity increases at the same rate, and vice-versa. Clearly state your answer (Yes/No) and provide a concise reason.

Question 3. Can you give examples from science or everyday life of quantities that vary in direct proportion? (Textbook pg. no. 63)
Answer: 
1. Number of chairs and the number of spectators.
2. Quantity (litres) of water and number of vessels required to store the water.
In simple words: प्रत्यक्ष अनुपात के उदाहरणों में कुर्सियों की संख्या और दर्शकों की संख्या, या पानी की मात्रा और उसे स्टोर करने के लिए आवश्यक बर्तनों की संख्या शामिल है।

🎯 Exam Tip: Provide clear and distinct examples. Ensure that for each example, if one quantity increases, the other quantity also increases proportionally, illustrating the concept of direct variation.