Chapter 9 Direct Proportion and Inverse Proportion Practice Set 39 Solutions

Total investment = Rs 144000 Profit earned = 20% ∴ Total profit = 20% of 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 ∴ 9x = 28800 ∴ = 3200 ∴ Suresh’s profit = 4x = 4 × 3200 = Rs 12800 Ramesh’s profit = 5x = 5 × 3200 = Rs 16000 ∴ The profit earned by Suresh and Ramesh are Rs 12800 and Rs 16000 respectively.

Total investment = Rs 50000 + Rs 120000 = Rs 170000 Loss incurred = 20% ∴ Total loss = 20% of 170000 = = Rs 34000 Proportion of investment = 50000 : 120000 = 5 : 12 …. (Dividingby 10000) Let the loss incurred by Virat be Rs 5x and that by Samrat be Rs 12x. 5x + 12x = 34000 ∴ 17x = 34000 ∴ ∴ Virat’s loss = 5x = 5 × 2000 = Rs 10000 Samrat’s loss = 12x = 12 × 2000 = Rs 24000 ∴ The loss incurred by Virat and Samrat are Rs 10000 and Rs 24000 respectively.

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% ∴ Total profit = 24% of 80000 = x 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 ∴ 40x = 19200 ∴ ∴ Nachiket’s profit = 19x = 19 × 480 = Rs 9120 ∴ Nachiket’s investment is Rs 38000 and his profit is Rs 9120.

Proportion of share = 3:7 Let the profits of A and B be Rs 3x and Rs 7x respectively. 3x + 7x = 24500 ∴ 10x = 24500 ∴ Profit earned by A = 3x = 3 × 2450 = Rs 7350 Amount given by A = 2% of his profit = × 7350 = Rs 147 Profit earned by B = 7x = 7 × 2450 = Rs 17150 Amount given by B = 2% of his profit = × 17150 = Rs 343 ∴ The amount given by A and B to the Soldiers’ Welfare Fund are Rs 147 and Rs 343 respectively.

Total investment = Rs 360000 Profit earned = 12% ∴ Total profit = 12% of 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 ∴ 20x = 360000 ∴ = 18000 ∴ Jaya’s investment = 3x = 3 x 18000 = Rs 54000 Also, profit made by them is Rs 43200 ∴ 3x + 4x + 7x + 6x = 43200 ∴ 20x = 43200 ∴ = 2160 ∴ Nikhil’s profit = 7x = 7 x 2160 = Rs 15120 ∴ Jaya’s share in the capital was Rs 54000 and the profit made by Nikhil was Rs 15120.

Total investment = Rs 2400 + Rs 5200 + Rs 3400 = Rs 11000 Total profit = 50% of 11000 = = Rs 5500 Proportion of shares = 2400 : 5200 : 3400 = 12 : 26 : 17 …. (Dividingby 200) Let the profit of Saritaben, Ayesha and Meenakshi be Rs 12x, Rs 26x and Rs 17x respectively. 12x + 26x + 17x = 5500 ∴ 55x = 5500 ∴ x = 100 ∴ Saritaben’s profit = 12x = 12 × 100 = Rs 1200 Ayesha’s profit = 26x = 26 × 100 = Rs 2600 Meenakshi’s profit = 17x = 17 × 100 = Rs 1700 ∴ Saritaben’s new investment = 2400 + 1200 = Rs 3600 Ayesha’s new investment = 5200 + 2600 = Rs 7800 Meenakshi’s new investment = 3400 + 1700 = Rs 5100 ∴ New proportion of shares = 3600 : 7800 : 5100 = 12 : 26 : 17 …. (Dividing by 300) ∴ The proportion of the shares in the capital during the following year is 12 : 26 :17

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.