Two MIT math graduates bump into each other at Fairway on the upper west side. They hadn't seen each other in over 20 years. The first grad says to the second: "how have you been?" Second: "Great! I got married and I have three daughters now" First: "Really? how old are they?" Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there.." First: "Right, ok.. oh wait.. hmmmm.., I still don't know" second: "Oh sorry, the oldest one just started to play the piano" First: "Wonderful! my oldest is the same age!" Problem: How old are the daughters?
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2. You are required to prepare a Profit & Loss Account for the year ending 31st December, 2007 and the Balance Sheet on that date. The Trial Balance of XYZ Ltd. for the year ended 31st December 2007 is as follows:- Trial Balance of XYZ Ltd. as on 31st Dec. 2007 Debit Balances Rs. Credit Balances Rs. Materials used 3,50,000 Sales(including 2% Sales tax) 9,18,000 Cost of Labour 1,50,000 Sale of Scrap 100 Stock, finished and work in process on 31st December, 2006 50,000 Rent received 2,000 Wages : Factory Staff 15,000 Discounts 2,750 Directors Remuneration 50,000 Recovered against fire claim re : Stock 5,000 Salaries : Clerical Staff 75,000 Capital : Equity 25,000 Insurances : Workmen’s Compensation 1,500 Preference- 9% 8,000 General, fire etc. 2,000 Creditors 1,56,000 Directors’ Life Insurance 1,500 Provision for Taxation 1,05,000 Maintenance : Buildings 1,000 Profit & Loss Account 13,750 Plant and Machinery 12,500 Rent and Rates of premises and hire of plant 20,000 Heat, Light and Power 15,000 Experimental and Laboratory Expenses 10,000 Canteen Expenses 5,000 Staff Welfare expenses 2,500 Motor Expenses 12,500 Professional Charges 2,800 Postage and Telephone 3,500 Books, Printing and Stationery 11,000 Sundry expenses 10,000 Carriage and Packing on Sales 3,300 Discounts 5,000 Debtors 1,78,000 Freehold Property 50,000 Plant and Machinery 12,500 Fixtures and Fittings – Offices 3,500 Office machinery and Equipment 3,000 Motor Car and Van 6,500 Stock of materials on 31st Dec. 2007 1,20,000 Bank 38,000 Sales Tax Paid 15,000 12,35,600 12,35,600 Depreciation is to be provided at the following rates: Plant and Machinery 10% Fixture and Fittings 05% Office Machinery, etc. 10% Motor Vans and Cars 25% The stock of finished goods and work in progress as on 31st December, 2007 was Rs. 35,000. Provide for preference dividend and ordinary dividend at 10%. The total taxation liability is estimated at Rs.1,50,000 of which Rs. 75,000 relates to the current year. Debtors include Rs. 10,000 deposited as security against government contracts. The Works Manager is paid partly by salary and partly by a commission; he is entitled to a commission of 5% on the amount by which the surplus in the factory cost exceeds 20% of the sales for the period. Charge the commission if any in the Profit and Loss Account.
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5. Two long boundary walls run parallel to each other at a center to center distance of 1 meter apart. The width and height of the first wall are 0.30 m and 2.5m respectively. While those of the second are respectively 0.18m and 3.5m. Plot the distribution of vertical stress intensity due to walls on a horizontal plane, 1m below ground level. The walls have negligible depth of foundation and are made of brick masonry (y = 19.2 kN/m cu)