Skip to content

Unique Paper Code 7352

Revised 0 of 18

Business MathematicsDecember 2025

B.Com (Hons) · 5 questions · 2 parts still being checked

Duration: 3 HoursMaximum Marks: 90

Reworded by Kunji from the printed paper. The original paper belongs to the University of Delhi. See DU's question bank.

Before you start

Most asked here. Partial differentiation and production functions (3 papers), Maxima and minima in one variable (3 papers), Matrices and determinants (3 papers). These come back almost every year, so learn them first. The asked N× note beside each part counts the DU papers that set its topic.
Pace. Two minutes a mark: about 36 minutes for each 18-mark question, with nothing spare in 3 hours. Pick your side of each OR before you start writing.
Keep score. Every part opens a worked answer checked against the books. Turn the key when you have revised it; the boxes at the top fill in, on this device.

1.

18 marks
· ~36 min

(a)Two industries: new gross outputs, labour days, value added and viabilityasked 3×The input-output relationship (in units) of two industries is shown below : Using matrix notation, determine: (i) Gross output needed to meet the new final demand of 132 units for industry I and 264 units for industry…(12)

(b)Depreciation schedules of two machines in matrix notationasked 3×A firm buys two machines, at a cost of ₹41,000 and ₹45,000 respectively. Each machine has a useful life of 4 years and zero salvage values at the end of 4 years. Using matrix notation, find the depreciation of each…(6)

OR

(a)Three-sector economy: gross outputs for a final demand and for its increaseasked 3×The input-output coefficients aᵢⱼ of a three-sector economy are : a₁₁ = 0.4, a₂₁ = 0.1, a₃₁ = 0.2, a₁₂ = 0.2, a₂₂ = 0.5, a₃₂ = 0.1, a₁₃ = 0.2, a₂₃ = 0.1, a₃₃ = 0.5. (i) Determine the gross output of each of the three…(12)

(b)Daily output of three products from machine hours (matrix inverse)asked 3×A firm makes three products X, Y and Z, each processed by three machines M₁, M₂ and M₃ until complete. M₁ can process 30 units of X or 60 units of Y or 90 units of Z per hour. M₂ can process 60 units of any one product…(6)

2.

18 marks
· ~36 min

(a)Elasticity of supply and income elasticity of demandasked 2×For the supply function x = 2 p² + 7, find the elasticity of supply when p = 4. (ii) Demand x depends on income y through 40 x = 20 + 2 y. Calculate the value of the income elasticity of demand when y = 250.(9)

(b)Optimal replacement time of a machineasked 3×A machine costs ₹12,480. Up to a time t from the date of purchase, the total cost of operation is given by the function: 70 t² + 0.3 t. If the machine is sold as scrap after t years, its resale value is described by the…(9)

OR

(a)Profit-maximising output from a demand curve and an average cost curveasked 3×A firm faces the demand curve x = 240 - 3 p and the average cost curve AC = 10 + x/60, where p denotes the price per kg and x the output (in kg). Determine the output that gives the maximum profit. Calculate the…(9)

(b)Four partial elasticities of demand and the nature of the two commoditiesasked 3×The demand functions for two commodities are : Q₁ = 1800 + 300/(p₁+2) - 40 p₂ and Q₂ = 1800 + 450/(p₁+5) - 80 p₂. (i) Calculate all four partial elasticities of demand at p₁ = 4 and p₂ = 2. (ii) Comment on the nature of…(9)

3.

18 marks
· ~36 min

(a)Cobb-Douglas Q = 36L^(3/5)K^(2/5): marginal products, returns to scale and factor rewardsasked 3×A production function is given by Q = 36 L^{3/5} K^{2/5}, where L denotes the units of labour and K the units of capital. (i) Find how the marginal product of each factor behaves. (ii) What is the nature of the returns…(9)

(b)Demand function from its price elasticityasked 3×The price elasticity of demand for a commodity is Eₚ = P/[(P - 2)(P - 3)], where P is the price per unit. Obtain the demand function that corresponds to a demand of 6 units when the price is ₹4. The same question was…(9)

OR

(a)Elasticity of substitution of a CES production functionasked 3×Find the elasticity of substitution of the following function : Q = 60(0.4 K^{-05} + 0.6 L^{-05})^{-20}(9)

(b)Producer's surplus two ways for the supply law 64p = (x + 20)²asked 3×If the supply function for a particular commodity is 64 p = (x+20)² and the market price is ₹36, find the producers surplus in two ways: (i) Integrate with respect to x, (ii) Integrate with respect to the price p.(9)

4.

30 marks
· ~60 min

(a)Compound amount under two successive rates and compounding periodsasked 3×Solve any three : (a) A man made a deposit of ₹3000 in a savings account. The deposit was left to accumulate at 8% compounded quarterly for the first 6 years and at 10% compounded semiannually for the next 9 years. Find…(6)

(b)Replacing three payments by a single sum: finding its due date at 10% effectiveasked 3×The sums of ₹2400, ₹3600 and ₹4800 fall due at the end of 3, 5 and 9 years respectively. It is proposed to replace this series of payments with a lump sum of ₹10800 payable at the end of n years. With the rate of…(6)

(c)Rate of depreciation from cost, scrap value and lifeasked 3×A machine costing ₹6400 will depreciate to a scrap value of ₹2302 in 8 years. Find the rate of depreciation.(6)

(d)Present value of a deferred monthly annuity at an annual compounding rateasked 3×Find the present value of an annuity consisting of 35 monthly payments of ₹150 each, the first being made at the end of 3 years and money is worth 8% compounded annually.(6)

(e)Machine A or Machine B: present value of labour savings at 12%asked 3×Machine A costs ₹12,000 and has a useful life of 9 years. Machine B costs ₹9000 and its useful life is 6 years. Machine A generates annual labour savings of ₹2400, whereas machine B generates an annual labour savings of…(6)

5.

18 marks
· ~36 min

Office furniture: formulating the LPP and solving it by the simplex methodBeing checked

(18)

OR

(a)Two types of pens: formulating the profit-maximising LPPasked 3×A company makes two types of pens, A and B. Pen A is of superior quality, while Pen B is of lower quality. The net profits on pen A and pen B are ₹60 and ₹40 respectively. The raw material needed for pen A is twice that…(6)

(b)

Reading a simplex table: completion, optimality, degeneracy, shadow pricesBeing checked

(12)

— End of the paper —