8. (1) Area of hole= (1 × 12) cub. in. 12 cub. in. Area of base of cylinder=(in.): .. volume of cylinder = × 3.14159; 12 x 3.14159 4 cub. in. =9.42477 cub. in.; .. part of hole unoccupied (12-9-42477) cub. in. =2.57523 cub. in. =rather more than 2 cub. in. (2) The Cambridge crew pulled 975 strokes in 25'. The Oxford crew lose by 1 of an Oxford stroke; .. 1026: 1 :: 4 mi.: distance by which race was won; 19 .. distance in feet= 1 × 4 × 1760 × 3 2713. Again, 1025 1: 25': time by which race was lost; 1. (1) Solid content of foundations =2(60 × 13 × 2+36 × 1 × 13) cub. ft. 2. (1) Log 144=log 32 × 24-2 log 3+ 4 log 2 =2 x 4771213+4 x 3010300 =9542426+1.2041200 =2.1583626. log 14.4=log 144-1=1.1583626. log 0144 log 144-4=2·1583626. log 168=log (7 × 3 × 8) = log 7+ log 3+3 log 2 =8450980+4771213 +9030900 =2.2253093. log 14700=log (72 × 3 × 100) =2x8450980+4771213+2 =1.6901960+2.4771213 = 4.1673173. (2) Content of cubical vessel = (3 × 3 × 3) or 27 cub. ft.; .. content of 2nd vessel 81 cub. ft.; 81-000000000 (4.32... ft. 3 x 42-48 3 × (40)2=4800 3 x 40 x 3 = 360 32= 5169 15507 64 17000 15507 3. (1) 10 men and 14 women earn £15. 6s. in 6 days, 10 men and 15 women earn £15. 15s. in 6 days; .. 1 woman earns 9s. in 6 days; .. 1 woman earns 1s. 6d. in 1 day. 2 men and 3 women earn 10s. 6d. in 1 day; .. 2 men earn 10s. 6d. – 4s. 6d. or 6s. in 1 day; .. 1 man earns 3s. in 1 day; ... 6 men and 12 women earn 18s. +18s. or 36s. in 1 day; (3) 2×3+3×6+4×8=6+13+32=56; .. 56 6 4s. 8d. cost of flour; : .. cost of flour=6d.; similarly, cost of raisins=1s. 6d., and cost of suet=2s. 8d. .. a circuitous remittance will be the most advantageous. 3 of £18550-£7420, and of £18550-£11130, £96 £7420 :: £4: income, .. whole income in 2nd case= £680. 3s. 4d.; £92 £18550 :: £3: income in 1st case, : 5. (1) Barley costs 50s. 10d. x 621=378810d.; To realize a profit of 5 per cent., barley must sell for 378810d. +18940 5d. or 397750.5; again, tax +5 per cent. on it=290d. +14.5d. =304 5d.; selling price of malt per quarter less tax and profit on it .. no. of quarters of malt=397750-5÷621 .. B earns (48. 2d. - 2s. 6d.) or 18. 8d. in 1 day, C..... (38. 10d.-2s. 6d.) or 1s. 4d. ...... |