Paper 4: Fundamentals of Business Mathematics & Statistic

1.4 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

Let the incomes be 4x and 3x (in `)

Now 4x 1000 33x 1000 2−− = or, x = 1000 (on reduction)

∴ Income of A = ` 4000, that of B = ` 3000.

Example 9 : The prime cost of an article was three times the value of material used. The cost of raw

materials was increased in the ratio 3 : 4 and the productive wage was increased in the ratio 4 : 5. Find the

present prime cost of an article, which could formerly be made for ` 180.

Prime cost = x + y, where x = productive wage, y = material used.

Now prime cost = 180 =3y or, y = 60, again x + y = 180, x = 180–y = 180–60 = 120

Present material cost = 4y 3 , present wage = 5x 4 ,

∴ Present prime cost =^4 × 3 60 5 120+ × 4 =80 150 230.+ =`

SELF EXAMINATION QUESTIONS :

1. The ratio of the present age of a father to that of his son is 5 : 3. Ten years hence the ratio would be
   3 : 2. Find their present ages. [Ans. 50,30]


2. The monthly salaries of two persons are in the ratio of 3 : 5. If each receives an increase of 20 in salary, the ratio is altered to 13 : 21. Find the respective salaries. [Ans. 240, ` 400]


3. What must be subtracted from each of the numbers 17, 25, 31, 47 so that the remainders may be in
   proportion. [Ans. 3]


4. In a certain test, the number of successful candidates was three times than that of unsuccessful
   candidates. If there had been 16 fewer candidates and if 6 more would have been unsuccessful, the
   numbers would have been as 2 to 1. Find the number of candidates. [Ans. 136]


5. (i) Monthly incomes to two persons are in ratio of 4 : 5 and their monthly expenditures are in the
   ratio of 7 : 9. If each saves 50 a month, find their monthly incomes. [Ans. 400, 500] (ii) Monthly incomes of Ram and Rahim are in the ratio 5 : 7 and their monthly expenditures are in the ratio 7 : 11. If each of them saves 60 per month. Find their monthly income.
   [Ans. 200, ` 280]

hints^5 x 60 7 &etc.

7x 60 11

− =

(^) − (^)

6. A certain product C is made or two ingredients A and B in the proportion of 2 : 5. The price of A is
   three times that of B.
   The overall cost of C is 5.20 per tonne including labour charges of 80 paise per tonne. Find the cost A and B per tonne. [Ans. 8.40, ` 2.80]


7. The prime cost of an article was three times than the value of materials used. The cost of raw materials
   increases in the ratio of 3 : 7 and productive wages as 4 : 9. Find the present prime cost of an article
   which could formerly be made for 18. [Ans. 41]