Paper 4: Fundamentals of Business Mathematics & Statistic

2.22 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

12. The expenses of a boarding house are partly fixed and partly varies with the number of boarders. The
    charge is 70 per head when there are 20 boarders and 60 per head when there are 40 boarders.
    Find the charge per head when there are 50 boarders.
    [hints refer solved ex. 55] [Ans. ` 58]

OBJECTIVE QUESTIONS

1. If A varies inversely with B and if B = 3 then A = 8, then find B if A = 2 [Ans. 12]


2. A is proportional to the square of B. If A = 3 then B = 16 ; find B if A = 5. [Ans.^4009 ]


3. A varies inversely with B and if B = 3 then A = 7. Find A if B =2.^13 [Ans. 9]


4. If x ∝ y and x = 3, when y = 24, then find the value of y when x = 8. [Ans. 64]


5. A varies inversely with B and B = 10 when A = 2, find A when B = 4. [Ans.5]


6. If y ∝x^12 and x = 2 when y = 9, find y when x = 3. [Ans. 4]


7. If A ∝ B, A = 7 when B = 21. Find the relative equation between A and B. [Ans. A = B^13 ]


8. If x varies inversely with y, x = 8 when y = 3, find y when x = 2 [Ans. 12]


9. If p ∝ q^2 and the value of p is 4 when q = 2, then find the value of q + 1 when the value of p is 9.
   [Ans. – 2]


10. If a + b ∝ a – b, prove that a ∝ b
    [hints : a + b = k (a – b), (1 – k) a = (– k – 1) b & etc.


11. If x varies as y then show that x^2 + y^2 varies as x^2 – y^2


12. If (a + b) varies as (a – b), prove that a^2 + b^2 varies as b^2


13. If a + 2b varies as a – 2b, prove that a varies as b


14. x and y are two variables such that x ∝ y. Obtain a relation between x and y if x = 20. Y = 4.
    [Ans. x = 5y]