Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.

8. There has been increment in the wages of labourers in a factory in the ratio of 22 : 25, but there has
   also been a reduction in the number of labourers in the ratio of 15 : 11. Find out in what ratio the total
   wage bill of the factory would be increased or decreased. [Ans. 6 : 5 decrease]


9. Three spheres of diameters 2, 3 and 4 cms. respectively formed into a single sphere. Find the diameter
   of the new sphere assuming that the volume of a sphere is proportional to the cube of its diameter.
   [Ans.^381 cm ]
   OBJECTIVE QUESTIONS :


10. Find the ratio compounded of 3 :7, 21 : 25, 50 : 54 [Ans. 1 : 3]


11. What number is to be added to each term of the ratio 2 : 5 to make to equal 4 :5. [Ans. 10]


12. Find the value of x when x is a mean proportional between : (i) x–2 and x+
    (ii) 2 and 32 [Ans. (i) 3 (ii) ± 8]


13. If the mean proportional between x and 2 is 4, find x [Ans. 8]


14. If the two numbers 20 and x + 2 are in the ratio of 2 : 3 ; find x [Ans. 28]


15. If
    a b 1finda
    a b^2 b

− =

+ [Ans.9]

7. If 3, x and 27 are in continued proportion, find x [Ans. ± 9]


8. What number is to be added to each term of the ratio 2 : 5 to make it 3 : 4? [Ans. 7]

Hints :2 x 3& etc.

5 x 4

+ =

(^) + (^)

9. If aa b+−b=^2 find the value of

2 2

2 2

a ab b

a ab b

− +

+ + [Ans.

7

13 ]

10. If 4x 3y 4z 3y 4y 3x4c− = 3b− = 2a− show that each ratio is equal to 2a 3b 4cx y z++ ++

Hints : each ratio^4 x 3z 4z 3y 4y 3x& etc.

4c 3b 2a

(^) = − + − + −
(^) + + (^)

11. The ratio of the present age of mother to her daughter is 5 : 3. Ten years hence the ratio would be
    3 : 2. Find their present ages. [Ans. 50; 30 years]


12. If A : B = 2 : 3, B : C = 4 : 5 and A : C [Ans. 8 :15]


13. If x : y = 3 : 2, find the value of (4x–2y) : (x + y) [Ans. 8 : 5]


14. If 15 men working 10 days earn 500. How much will 12 men earn working 14 days? [Ans. 560]


15. Fill up the gaps :
    a a 1 – b^22
    b= − =−= 1 = − [Ans. ab,
    b a,a b,b a,in order]^3


16. If x, 12, y and 27 are in continued proportion, find the value of x and y [Ans. 8 ; 18]


17. If
    x 3,
    y 4= find the value of

7x 4y

3x y

−

+ [Ans.

5

13 ]