The table below, Gives the marks of obtained by six students P,Q,R,S,T in five subjects A,B,C,D,E.
a, b, c, d, e denote the minimum marks scored in the A,B,C,D,E respectively
Max marks =100

A B C D E
P a+15 b+5 c d+4 e+1
Q a+14 b+8 c+5 d+2 e+2
R a+13 b+2 c+6 d+5 e
S a b+1 c+7 d+6 e+3
T a+8 b+4 c+3 d+3 e+6
U a+5 b c+9 d e+9

Also the following information is known
T scored equal marks in A and C
R scored one mark less in B than T scored in D
P scored 2 marks more in E then Q scored in B
The sum of of all the marks scored all the students in all subjects was 2600.
No one score less than 75 in any subject.

Questions:-
1)If U’s score in B was not less than P’s score in C, then how much did S score in E?
a)91 b)93 c)87 d)90
2)Referring to the previous question, who scored the max in which subject?
a)P,A b)Q,B c)U,E d)U,C
3)If P’s marks in A more than the marks anyone got in other subject, Then how much could T have scored In D?
a)64 b)83 c)82 d) 79
4)Which of the following cannot be R’s score in C?
a)94 b)90 c)93 d)96

• 1.a+8=c+3
  c-a=5
  2.d+3-(b+2)=1
  d-b=0
  d=b
  3.(e+1)-(b+8)=2
  e-b=9
  e-d=9
  4.(6a+55)+(6b+20)+(6c+30)+(6d+20)+(6E+21)=2600
  6(a+B+C+D+E)+146=2600
  6(a+B+C+D+E)=2600-146
  a+b+c+d+e=2454/6=409
  Min marks by each student is 75
  if a =75 then c=80 also b=80 d=80 then e=89
  but their sum is 404
  so adding 1 to each quantity we get sum
  a =76,b=c=d=81,e=90
  
  question 1st
  U's score in B= P's score in C
  i.b=c
  then S's score in e = e+3=90+3=93
  thus answer is b 93
  question 2nd
  from the above calculations we observed that e has scored max i.e 90 and U score in E is e+9 =90+9=99(max)
  Thus anwer is cU,E
  question 3rd
  it is given that p got max marks in A thus min marks is 75 sum of marks 409
  taking e=90 so max value e+9=90+9=99 which must be less than p+15(since it is biggest)
  p+15>99
  p+15=100
  so solving equation for t
  100+8+D+4+D+3+D+3+90+6=409
  -214+3D=409
  -d=82*3=246
  d=82
  answer is c
  Question 4
  r's score in c cannot be 94 is score is 94 c=88,if c=88, a =83,e=97
  d+3
• 11 years agoHelpfull: Yes(19) No(11)
• sravan can u plz send ur mobile no.. i want to talk to u about elitmus plzzzz. help me
• 11 years agoHelpfull: Yes(6) No(2)
• With the given information----------
  
  a = c - 5 ----------------- (1)
  d = b --------------------(2)
  e = b + 9 --------------------(3)
  and
  a + b + c + d + e = 409 ------------------(4) { adding all the marks }
  also
  a,b,c,d,e > = 75
  Now coming to the first question------------
  Relation between 'b' and 'c' is given , Thus convert equation (4) in 'b' and 'c' using (1) (2) (3)---
  
  We get , 3b + 2c = 405 ----------(5)
  
  Now either b = c OR b > c ( according to question )
  --------------Now friends , here comes the main logic ----------------
  
  a = c - 5 , We know that 'a' must be least 75 , hence c must be least 80
  
  In (5)
  CASE 1 , if c = 80 then b = 81. 6 ( b > c , but decimal hence reject }
  
  CASE 2 if c = 81 then b = 81 ( b = c }
  
  CASE 3 if c = 82 then b = 80.3 { b < c reject}
  
  Hence , only possible solution is b = c = d = 81
  
  a = 76 and e = 90
  
  ANS 1 e + 3 = 93
  
  ANS 2 we can easily see that e + 9 is maximum , hence ( U , E }
  
  ANS 3 -----We have to check all the options to check for invalid options ----
  
  Now maximum marks are 100 , hence a + 15 < 100 ,---------- 75 < a < 85 ---------
  
  T Score is d + 3
  
  (a) # Cannot be 64 ( INVALID )
  
  (b) 83 , i.e d = 80 , Now using (1) (2) (3) (5) , We get d = b = 80 , e = 89 c = 82.5 ( INVALID )
  
  (c) 82 , i.e d = 79 , ( d = b = 79 , e = 88 and c = 84 , a = 79 ) -------- ( VALID )
  
  (d) 79 , i.e d = 76 , ( d = b = 76 , e = 85 and c = 83.5 ( INVALID )
  
  Hence (c) 82 is correct
  
  ANS 4 ---Do it yourself-----
  
  
• 9 years agoHelpfull: Yes(4) No(0)
• a=76
  b=c=d= 81
  e= 90
• 11 years agoHelpfull: Yes(2) No(2)
• 1.b
  2.c
  3.c
  4.a
• 11 years agoHelpfull: Yes(1) No(0)
• Table:
  
  A B C D E
  
  P a+15 b+5 c d+4 e+1
  
  Q a+14 b+8 c+5 d+2 e+2
  
  R a+13 b+2 c+6 d+5 e
  
  S a b+1 c+7 d+6 e+3
  
  T a+8 b+4 c+3 d+3 e+6
  
  U a+5 b c+9 d e+9
• 11 years agoHelpfull: Yes(0) No(2)
• BANKIM can u explain how?
• 11 years agoHelpfull: Yes(0) No(2)
• 9618476235
  
• 11 years agoHelpfull: Yes(0) No(3)
• please anybody explain its proper solution
• 11 years agoHelpfull: Yes(0) No(1)
• @sumit what if we take the value of a=75, b=80,c =84,d=80, e=89
  therefore , by adding a+b+c+d+e = 408 . hence we will add 1 to c to make the total 409 i.e c=84+1=85
  A/Q e+3 =? ; e+3= 89+3=92 .
• 11 years agoHelpfull: Yes(0) No(0)
• @sumit how b=c??
• 9 years agoHelpfull: Yes(0) No(0)
• @Ajitesh,
  in http://www.m4maths.com/18178-The-table-below-Gives-the-marks-of-obtained-by-six-students-P-Q-R-S-T-in-five-subjects-A.html#
  question 3, we can't assume that the condition given in the 1st question (b>=c), will be valid, unless stated.
  
  then why did we rule out case of
  
  a=82 b=77 c=87 d=77 e=86
  a=85 b=75 c=90 d=75 e=84
  
  Moreover, the solution you assumed for ques 3, a=79 b=79 c=84 d=79 e=88, it negates the statement that P scored the highest in A (a+15=94) than any other student in any other subject, as then T will have e+9=97 in E.
  
  please clarify?
• 8 years agoHelpfull: Yes(0) No(0)