Ajay working in a Cellular company as a salesman. His monthly salary is Rs. 200. But he gets bonus as per given rule. If he sells sim cards of Rs. X then his bonus will be $$\left[ {{{\left( {\frac{x}{{100}}} \right)}^2} + 10} \right]$$ . In the first quarter of the year his average sale was Rs. 3000 per month. In the next 5 five month his average sale was Rs. 5000 per month and for next four month his average sale was Rs. 8000 per month. What is the average earning per month for the whole year?
A. Rs. 3350
B. Rs. 3610
C. Rs. 3750
D. Rs. 3560
E. None of these
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Bonus}}\,{\text{for}}\,{\text{the}}\,{\text{first}}\,{\text{three}}\,{\text{month}}, \cr & = \left[ {{{\left( {\frac{{3000}}{{100}}} \right)}^2} + 10} \right] \times 3 \cr & = Rs.\,2710 \cr & {\text{Bonus}}\,{\text{for}}\,{\text{the}}\,{\text{next}}\,{\text{five}}\,{\text{month}}, \cr & = \left[ {{{\left( {\frac{{5000}}{{100}}} \right)}^2} + 10} \right] \times 5 \cr & = Rs.\,12550 \cr & {\text{Bonus}}\,{\text{for}}\,{\text{the}}\,{\text{next}}\,{\text{four}}\,{\text{month}}, \cr & = \left[ {{{\left( {\frac{{8000}}{{100}}} \right)}^2} + 10} \right] \times 4 \cr & = Rs.\,25640 \cr & {\text{Total}}\,{\text{earning}}\,{\text{as}}\,{\text{bonus}}\,{\text{for}}\,{\text{whole}}\,{\text{year}}, \cr & = 2710 + 12550 + 25640 \cr & = Rs.\,40900 \cr & {\text{His}}\,{\text{average}}\,{\text{bonus}} \cr & = \frac{{40900}}{{12}} = Rs.\,3410 \cr & {\text{Thus}}\,{\text{his}}\,{\text{average}}\,{\text{earning}}\,{\text{for}}\,{\text{whole}}\,{\text{year}}, \cr & = 3410 + 200 \cr & = Rs.\,3610 \cr} $$This Question Belongs to Arithmetic Ability >> Average
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How can you solve it like this because if you solve it through detail like for first 3 month his total sale will be 9000 for next 5 month it will be 25000 and for mext 4 month it will be 32000 then from this method one can not find the right answer why?
Total selling in 12 moths be 66000,
(3000*3=9000
5000*5+25000
8000*4=32000)
_____________
then monthly selling be 66000/12
then his bonus be (66000/(12*100))^2+10=2714
Now his monthly salary is 200
now his avarage earning per month be 2714+200=Rs. 2914
For twelve months he sold Total
= 3*3000+5*5000+4*8000
So get bonus in Twelve months
= 3[(3000/100)^2 + 10] + 5[(5000/100)^2 + 10]
+ 4[(8000/100)^2 + 10]
= 3*30^2 + 5*50^2 + 4*80^2 + 120
= 3*900+5*2500+4*6400+120
= 40920
Average bonus = 40920/12 = 3410
Average earnings per month
= 3410+200 = 3610
Bonusforthefirstthreemonth,
=[(3000100)2+10]×3=Rs.2730
Bonus for the first three month,
= [(3000 /100)2 +10] *3
= Rs. 2730.
Bonus for the next five month,
= [(5000 /100)2 +10] *5
= Rs. 12550.
Bonus for the next four month,
= [(8000 /100)2 +10] *4
= Rs. 25640.
Total earning as bonus for whole year,
= 2730 + 12550 +25640
= Rs. 40920.
His average bonus = 40920 /12 = Rs. 3410
Thus his average earning for whole year,
= 3410 + 200
= Rs 3610.