Chapter 9 Commercial Mathematics Miscellaneous Exercise 9 Solutions

Let ₹ ‘x’ be the annual rent of the house. The man keeps 10% of the annual rent aside for repairs. i.e., × x or ₹ aside tor repairs. In addition, he pays ₹ 1000 as annual taxes. After incurring these expenses he is left with an amount which is 8% of his investment for the house. ∴ The annual rent of the house is ₹ 90,000.

Let maximum marks be x Rose scored 30% of maximum marks i.e. Rose scored x Rose failed by 10 marks ∴ passing marks = x + 10 …..(i) Lily scored 40% of maximum marks i.e. Lily scored x Lily scored 15 marks more than passing marks ∴ passing marks = x – 15 ……(ii) equating (i) and (ii), + 10 = – 15 ∴ 10 + 15 = ∴ 10x = (25)(100) ∴ x = 250 From (i), passing marks = (250) + 10 = 75 + 10 = 85 ∴ Passing marks for the examination were 85.

Let Ankita’s initial salary be ₹ ‘x’. Her salary was reduced by 50%. ∴ Ankita’s salary after reduction = x(1 – ) = x(1 – ) = Ankita’s reduced salary was then increased by 50% ∴ Ankita’s final salary after the increase ∴ Loss in Ankita’s salary after the decrease and increase = x – = ∴ Ankita lost 25% of her salary.

Let ₹ x be the selling price (S.P.) of one lunch box. ∴ S.P. of 300 lunch boxes = 300x and S.P. of 100 lunch boxes = 100x Gain = 100x ……[given] C.P. of 300 lunch boxes = S.P. – Gain = 300x – 100x = 200x ∴ The shopkeeper’s gain percentage is 50%.

Let ₹ x be the cost price of the article. S.P. of the article = x – x = …….(i) Given that, S.P. increased by ₹ 80 would have given 10% gain ∴ The cost price of the article is ₹ 400

Let the marked price be ₹ 100 After 1st discount the price = 100(1 – ) = 90 After 2nd discount the price = 90(1 – ) = 72 After 3rd discount the price = 72(1 – ) = 61.2 ∴ The selling price after 3 discounts is ₹ 61.2. ∴ Single equivalent discount = marked price – selling price = 100 – 61.2 = ₹ 38.8 ∴ The single equivalent discount is ₹ 38.8 on ₹ 100. i.e. The single equivalent discount is 38.8%.

Let P and R represent the principal amount and rate of interest p.a. respectively. Given duration = T = 3 years Simple interest = Given that, had the amount been kept at 2% more, then the gain would have been ₹ 360 more. ∴ The sum of money is ₹ 6,000.

Given that, Principal (P) = ₹ 30,000 Rate of interest (R) = 7% p.a. Compound interest = ₹ 4,347 Amount after compound interest = = (1.07)2 ∴ T = 2 ∴ Amount is invested for 2 years.

Given, Rate of depreciation = r = 15% Number of years = n = 2 years Present value of machine = P.V. = ₹ 7,225 The purchase price (V) of the machine can be found using ∴ The purchase price of the machine was ₹ 10,000/-.

The height of the tree today is 8m. The height of the tree increases by th of its height every year. At the end of 1st year, height of the tree will be = 8 + × 8 = 9 m And, at the end of the 2nd year, height of the tree will be = 9 + × 9 = 9(1 + ) = 9 × = After six more months, the height of the tree will be ∴ Increase in the height of the tree after 2 years = 10.75 – 8 = 2.75 m.

Given, Value of the building = V.B. = ₹ 1,21,000 Value of land = V.L. = ₹ 81,000/- Rate of appreciation of land = rate of depreciation of building = r = 10%. For the value of building and land to be the same. ∴ n = 2 years. ∴ After two years value of the building and land will be the same.

Let ‘T’ be Varan’s total savings. ∴ Investment of Varan in: Company A = 25% of T = × T = , Company B = 30% of T = × T = , Company C = 20% of T = × T = Company A, B and C declared dividends 10%, 12% and 15% respectively. ∴ Dividend from company A = 10% of ∴ Varan invested ₹ 21,000 in company B.

Amount invested = ₹ 25,000 Dividend = 8% Assuming face value F.V. as ₹ 100 Annual income per share = = × 100 = ₹ 8 Market value of the share M.V. = ₹ 108 Annual dividend on amount invested = Rate of return × amount invested = × 25,000 = ₹ 1850 ∴ Annual dividend of ₹ 1,850 is received from 8% stock at ₹ 108. Alternate approach Assuming ₹ 25,000 as the total face value of all the shares. Since the dividend is 8%, Annual dividend = × 25,000 = ₹ 2,000

Let ‘a’, ‘b’ and ‘c’ be the amounts invested by A, B and C respectively. Given that, A invests 3 times as much as B and B invests two third of what ‘C’ invests. ∴ a = 3b and b = c ∴ and or and ∴ a : b = 6 : 2 and b : c = 2 : 3 ∴ a : b : c = 6 : 2 : 3 Given that profit earned = ₹ 8800 ∴ Share of ‘B’ in profit = × 8800 = ₹ 1600 ∴ B’share in profit is ₹ 1600.

Let ‘x’ be the time in months for which Banta invested his money Santa and Banta invested their money in the ratio 11 : 12. Santa invested his money for 8 months and the ratio of their profits is 2 : 3. ∴ 11 × 8 : 12 × x = 2 : 3 ∴ ∴ x = ∴ x = 11 ∴ Banta invested his money for 11 months.

Let ‘R’ be the rent per month to be paid to the landlord. Given that, Sid left the house after 4 months ∴ Rent paid by Sid = × 4 = Sameer left the house after another 5 months, ∴ Rent paid by Sameer = × 5 + × 4 = R() = Akash stayed in the house for the entire year. ∴ Rent paid by Akash = 3R + × 5 + × 4 = R(3 + ) = ∴ The rent paid by the three of them, over that period of one year must be in the proportion. i.e. in the proportion 41 : 23 : 8 …..(multiplying throughout by ) Let x be the constant of proportionality. Rent to be paid by Akash = ₹ 41x Rent to be paid by Sameer = ₹ 23x and rent to be paid by Sid = ₹ 8x The total rent for the house was ₹ 16236. ∴ 41x + 23x + 8x = ₹ 16236 ∴ 72x = 16236 ∴ x = 225.5 ∴ Akash should pay 41x = 41 × 225.5 = ₹ 9245.5 Sameer should pay 23x = 23 × 225.5 = ₹ 5186.5 and Sid should pay 8x = 8 × 225.5 = ₹ 1804

Given, total sales amount for Ashwin Automobiles was ₹ 6,80,000. 18% GST is applicable. ∴ GST payable = 18% of 6,80,000 = × 6,80,000 = ₹ 1,22,400 Now CGST = SGST = 9% = = = ₹ 61,200 ∴ CGST = SGST = ₹ 61,200

Given that, stock purchased by ‘Sweet 16’ was worth ₹ 4,00,000 GST applicable is 12%. ∴ Input tax = 12% of 4,00,000 = × 4,00,000 = ₹ 48,000 ∴ Input tax Credit (ITC) = ₹ 48,000 The garment stock was sold for ₹ 5,50,000 Output tax = 12% of 5,50,000 = × 5,50,000 = ₹ 66,000 ∴ GST payable = output tax – ITC = 66,000 – 48,000 = ₹ 18,000 ∴ CGST = SGST = = ₹ 9,000