Question

A salesman used three types of order forms: A, B, C. He used 40 of Form A. Of Form B he used four times as many as Form A plus 1/2 as many as Form C. He used as many of Form C as Form A plus 1/2 as many as Form B. Altogether, how many forms did he use? Clear 0A. 440 B. 200 C. 250 D. 320 E. 500

Answer 1

The correct option is A. 440

Explanation:

Let a, b and c represents the number of orders from forms A, B and C,

According to the question,

`a = 40`,

`b = 4a + (1)/(2)c`

`c = a + (1)/(2)c`

From these equations we get,

`b = 160 + (1)/(2)c----(1)`

`c = 40 + (1)/(2)b---(2)`

Substitute the value of b from (1) to (2),

`c = 40 + (1)/(2)(160 + (1)/(2)c)`

`c = 40 + 80 + (1)/(4)c`

`c-(1)/(4)c = 120`

`(4c-c)/(4)=120`

`(3c)/(4)=120`

`c=(480)/(3)=160`

From (1),

`b = 160 + (1)/(2)(160)=160 + 80 = 240`

`\because a + b + c = 40 + 240 + 160 = 440`

Hence, he used 440 forms total,

i.e. OPTION A is correct.