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# Arithmetic Aptitude :: Simplification

Home > Arithmetic Aptitude > Simplification > General Questions

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41. One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt.Then find the price of the shirt.

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Explanation:

Servant (1 year) or (12 months) payment = (Rs. 200 + shirt) ------(1)
Servant recieve payment after 9 months = (Rs 120 + shirt) --(2)
By eq. (1) and (2)
3 months = Rs. 80
So, 12 months = (80 * 12)/3= 320
By eq. (1)
200 + shirt = 320
=> shirt price = Rs. 120

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Tags:  Accenture

42. If 2x+y = 11, 2y+z = 12 and z+2x = 8, find the value of 2x + 3y +4z.

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Explanation:

Without Finding x & y & z
2x+y = 11 -->(1) 2y+z = 12 -->(2) z+2x = 8 ---> (3)
(2)* 2=> 4y+2z=24-----(A)
(3)* 2=> 2z+4x=16-----(B)
(1)*-1=> -2x-y =-11-----(C)
2x + 3y +4z=29

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Tags:  Accenture

43. 5/11 of the paper produced can be recycled if 6,42,400 tonnes of paper is produced. what quantity of recycle of paper can be made after its use?

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Explanation:

642400*5/11=292000

Workspace

Tags:  Cognizant

44. Malini solved the following question in her Mathematics examination:

(6/4+5 ^1/6 of 3/7)/(5+2^1/3)

and her answer was 38/77. By how much was her answer wrong?

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Explanation:

6/4+(31/6 * 3/7) = 104/28

5 + 7/3 = 22/3

104/28 / 22/3 = 39/77

39/77 - 38/77 = 1/77

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Tags:  Cognizant

45. if x-y+z=19,y+z=20,x-z=3
find the value of x+4y-5z.

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Explanation:

Given:
x-y+z=19 -----(1)
y+z=20-----(2)
x-z=3-------(3)
By solving eq (1) & (2)
x-y-2z=-17-------(4)
By solving eq. (2) & (4)
z=12.
put the value of z in eq (2)
y=8
Similarly x=15

Put the value of x, y and z
x+4y-5z=15+32-60=-13.

Workspace

Tags:  Capgemini

46. Find min value of f(x) : |-5-x| + |2-x|+|6-x|+ |10-x|; where x is an integer

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Explanation:

Note: | a | = | ?a |
| ?5 ? x | = | ?(?5 ? x) | = | 5 + x | and
| 2 ? x | = | ?(2 ? x) | = | ?2 + x | = | x ? 2 |
=> | ?5 ? x | + | 2 ? x | + | 6 ? x | + | 10 ? x |
= | 5 + x | + | x ? 2 | + | 6 ? x | + | 10 ? x |
Also | a | + | b | ? | a + b | for all a and b
and | c | + | d | ? | c + d | for all c and d
and so:
| a | + | b | + | c | + | d | ? | a + b | + | c + d | ? | a + b + c + d |
| a | + | b | + | c | + | d | ? | a + b + c + d |

Therefore
| ?5 ? x | + | 2 ? x | + | 6 ? x | + | 10 ? x |
= | 5 + x | + | x ? 2 | + | 6 ? x | + | 10 ? x |
? | 5 + x + x ? 2 + 6 ? x + 10 ? x | = | 19 | = 19

Workspace

Tags:  Capgemini

47. Factorize y^2 + 8y - 48 = 0

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Explanation:

Solution:  y^2+ 8y-48=0

y^2+12y-4y-48=0

y(y+12)-4(y+12)=0

(y-4)(y+12)

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Tags:  CGI

48. How many 1's are there in the binary form of 8*1024 + 3*64 + 3

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Explanation:

8*1024 + 3*64 + 3 = 8387
= 10000011000011

Workspace

Tags:  CGI

49. In the following, which is the closest approximation of (50.2*0.49)/199.8 ?

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Explanation:

(50.2*0.49)/199.8 ~ (50*0.5)/200 = 0.125

Workspace

Tags:  TCS

50. If A=2/3(B-C) and c=1/2(A+B) and A+B+C=3000, then find C ?

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Explanation:

C=1/2(A+B)
A+B+(1/2(A+B))=3000
3/2(A+B)=3000
A+B=2000
C=1/2(A+B)
C=1000

Workspace

Tags:  TCS