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8. (1) Area of hole= (1 × 12) cub. in. 12 cub. in.

Area of base of cylinder=(in.):

.. volume of cylinder =

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× 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'.

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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
1026

2713.

Again, 1025 1: 25': time by which race was lost;

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1. (1) Solid content of foundations

=2(60 × 13 × 2+36 × 1 × 13) cub. ft.

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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)
=2log 7+ log 3+2

=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

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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;

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(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.

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.. a circuitous remittance will be the most advantageous.

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3
5

of £18550-£7420, and of £18550-£11130,

£96 £7420 :: £4: income,

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.. whole income in 2nd case= £680. 3s. 4d.;

£92 £18550 :: £3: income in 1st case,

:

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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

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.. no. of quarters of malt=397750-5÷621

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.. B earns (48. 2d. - 2s. 6d.) or 18. 8d. in 1 day,

C..... (38. 10d.-2s. 6d.) or 1s. 4d.

......

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