# Quantitative Ability Question

This quantitative ability question was sent to me by Mr. Satish Kumar by mail. I generally answer the questions I get on email by directly replying to them. However, I thought this question is worth to be discussed with all QM readers. So here it goes -

**Question**

I have a total of rs 1000. Item A costs rs 110,item B costs rs 90, item C costs rs 70 ,item D costs rs 40 and item E costs rs 45. For every item D that i purchase, I must also buy only 2 items of B. For every item A, I must buy one item of C. For every item E, I must also buy 2 of item D and one of item B. For every item purchased I earn 1000 points and for every rupee not spent I earn a penalty of 1500 points. My objective is to maximise the points I earn. What is the number of items that I purchase to maximise my points?

options….

a) 13 b)14 c)15 d)16

“Give me the procedure to solve this with in 2-3 mins . It takes to much time 2 solve this for me.” – Satish Kumar

Pay attention to Satish’s problem and suggest time reduction techniques along with the solution to the above problem.

I would latter include the best answer(s), posted as comment, in the post itself.

The answer is 14. 13 items C and one item B, that makes 13*70+1*90=1000 with no fine. It also satisfies all the condition.

Answer is a) 13.

2 of a = 180,

1 of b = 90,

1 of c = 70, and

3 of e = 660. Total 1,000

to get the ratio of A:B:C:D:E= 1:1:2:2:1

Sun of ratio= 7

which option is divisible by 7, that option is correct.

thanks..

I have a book “how to solve aptitude question by OPTION”

Could you please tell where can I get the book. I searched online but in vain. Any links?

how to get the ratio 1:1:2:2:1?

4E = 4*45 = 180

8D = 8*40 = 320

4B = 4*90 = 360

2C = 2*70 = 140

Thus we spend Rs. 1000 (no penalty) & 18 items gives us 18000 points.

I got the same answer. Why is it not in the options?

govibd chk d conditions also…….for evry D u have 2 purchase two items of B…so acc to u ,u purchased 8D so….B must be equal to 16

Answer is 14.

To purchase highest thing u have to purchase lowest cost things.now d=40 if we purchase 3d+6b+a+c+c+b=13 things.

E=45 is not possible because e+2d+4b+b=575 is not compenset .

Now c=70 purchase 13c+b=910+90=1000 for 14 things. So u have to purchase 13c+b=14 things.

Answer is 14.

To purchase highest thing u have to purchase lowest cost things.now d=30 if we purchase 3d+6b+a+c+c+b=13 things.

E=45 is not possible because e+2d+4b+b=575 is not compenset .

Now c=70 purchase 13c+b=910+90=1000 for 14 things. So u have to purchase 13c+b=14 things.

1. If 2B’s must be purchased for every D then 13C+1B = 14 items

2. If 2 B’s are sufficient for all D’s(because of “only 2 B” :)) then

2B+17D+2C = 21 items. But since its not an option, this can’t be true.

When you buy E, you end up buying 2D and 1B+ 3B(for the 2Ds that were purchased) which accounts to 485 and another E cannot be purchased since it takes the total to 970 which remains 30 which is bad. Even if you buy only 1E you still at the min remain with Rs.5 which is also bad.

So the only answer I see it 13c+1B. hence option b is the answer. hope so

4 items of E ……… 4*45 = 180 ………. Points 4000

8 items of D ……… 8*40 = 320 ………. Points 8000

4 items of B ……… 4*90 = 360 ………. Points 4000

2 items of C ……… 2*70 = 140 ………. Points 2000

===== ======

1000 18000

14 items – points earned = 14000

Take 13 items of C and 1 item of B

13*70+1*90= Rs 1000

ans is 15