Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.21

From (i), speed (s) = 24 2 n.− As n increases speed diministes,

For speed = 0, we have 0 24 2 h= − or, n 12= or, n = 144, i.e. when 144 wagons are attached engine
cannot move.
∴ Engine can move with 144 – 1 = 143 wagons.

SELF EXAMINATION QUESTIONS

1. Apply the principle of variation, how long 25 men take to plough 30 hectres, if 5 men take 9 days to
   plough 10 hectres of land? [Ans.^525 days]


2. The distance through which a heavy body falls from rest varies at the square of the time it falls. A body
   falls through 153 ft. in 3 secs. How far does it fall in 8 secs. And 8th sec? [Ans. 1,088ft. ; 255 ft.]


3. The time of the oscillation of a pendulum varies as the square root of its length. If a pendulum of length
   40 inch oscillates once in a second, what is the length of the pendulum oscillating once in 2.5 sec.?
   [Ans. 250 inch.]


4. The area of a circle varies directly with the square of its radius. Area is 38.5 sq. cm. when radius of the
   circle is 3.5 cm. Find the area of the circle whose radius is 5.25cm.
   [Ans.^8658 sq. cm.]


5. The volume of a gas varies directly as the absolute temperature and inversely as pressure. When the
   pressure is 15 units and the temperature is 260 units, the volume is 200 units. What will be volume when
   the pressure is 18 units and the temperature is 195 units? [Ans. 125units]


6. The expenses of a hotel are partly fixed and the rest varies as the number of boarders. When the
   number of boarders are 450, the expense is 1,800, when the number of boarders is 920, the expense is 3,210. Find the expenses per head when there are 100 boarders. [Ans. ` 34.50]


7. The total expenses of a hostel are partly constant and partly vary as the number of boarders. If the
   expenses for 120 boarders be 20000 and for 100 boarders be 17000, find for how many boarders will
   be ` 18800? [Ans. 112]


8. The expenses of a boarding house are partly fixed and partly vary with the number of boarders. The
   charge is 100 per head, when there are 25 boarders and 80 when are 50 boarders. Find the charge
   per head when there are 100 boarders. [Ans. ` 70]


9. The total expenses per pupil in a school consist of three parts, the first of which is constant, the second
   varies as the number of pupils and the third varies inversely as the number of pupils. When there are 20
   pupils, the total expenses per pupil are 744 ; when there are 30 pupils the total expenses per pupil are 564 ; when there are 40 pupils, the total expenses per pupil are 484 ; find the total expenses per pupil when there are 50 pupils. [Ans. 444]


10. As the number of units manufactured increases from 6000 to 8000, the total cost of production increases
    from 33,000 to 40,000.
    Find the relationship between y, the cost and x, the number of units made, if the relationship is linear.
    Hence obtain the total cost of production, if the number of units manufactured is 10000.
    [Ans. y = 12000 + 7/2 x : ` 47000]


11. Publisher of a book pays a lump sum plus an amount for every copy he sold, to the author. If 1000
    copies were sold the author would receive 2500 and if 2700 copies were sold the author would receive 5900. How much the author would receive if 5000 copies were sold?
    [hints refor solved ex. 54] [Ans. ` 10,500]