Latest TCS Aptitude Question SOLUTION: ab+a+b=250 bc+b+c=300 ca+a+c=216 find a+b+c??

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ab+a+b=250
bc+b+c=300
ca+a+c=216
find a+b+c??

Asked In TCS PRIYA NAMDEO (10 years ago)

Unsolved Read Solution (10)

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Read Solution (10) :

nirmit sabharwal  (10 years ago)

Answer is 45.25. Here is how I have done it. Please post any shortcut if available

ab + a + b = 250
a(1+b) + b = 250

a = (250−b)(1+b)

ac + a + c = 300
c(1+a) + a = 300

c = (300−a)(1+a)

=300−(250−b)(1+b)1+(250−b)(1+b)=300(1+b)−(250−b)1+b+250−b

=300(1+b)−(250−b)251=(50+301b)251=(50+301b)251

bc + b + c = 216

(50+301b)b251+b+(50+301b)251=216

(50 + 301b)b + 251b + 50 + 301b = 54216

301b2 +602b−54216 =0

b=12.46

a =(250−b)(1+b)=(250−12.46)(1+12.46) = 17.65
c = (300−a)(1+a)=(300−17.65)(1+17.65) = 15.14

These values of a,b and c statisfies the given conditions,as given below
ab + a + b = 17.65 *12.46 + 17.65 + 12.46 ≈ 250
ac + a + c = 17.65 *15.14 + 17.65 + 15.14 ≈ 300.21
bc + b + c = 12.46 *15.14 + 12.46 + 15.14 ≈ 216

Hence,
a + b + c = 17.65 + 12.46 + 15.14 = 45.25

Is this solution Helpfull? Yes (4) | No (6)  

Riya Khanna  (10 years ago)

ans 68
ab+a+b=250 ....1
bc+b+c=300 ....2
ca+a+c=216 ....3

multiply eq 1 by c, eq 2 by a and eq 3 by b
now solve 1 & 2, b=-50
2&3,c=84
3&1,a=34
34-50+84=68

Is this solution Helpfull? Yes (3) | No (17)  

Riya Khanna  (10 years ago)

sorry i did a mistake in my soln, the ans will be 45

Is this solution Helpfull? Yes (3) | No (3)  

prakher bhargava  (10 years ago)

pls tell what r the option...more then 1 option r possible...thats why i asked..i got 3 ans....

Is this solution Helpfull? Yes (1) | No (2)  

sprakash  (8 years ago)

Add 1 on both sides
ab+a+b+1=251==>(a+1)(b+1)=251--->1
bc+b+c+1=301==>(b+1)(c+1)=301--->2
ca+a+c+1=217==>(c+1)(a+1)=217--->3
Divide 1 by 2
(a+1)/(c+1)=0.83388==(a+1)=0.83388(c+1)--->4
from 3 (a+1)(c+1)=217, substitute 4 in 3
c=15.1315
by solving we get b=17.6590, a=12.4519
a+b+c=12.4519+17.6590+15.1315==45.24

Is this solution Helpfull? Yes (1) | No   

Prerna bisen  (5 years ago)

2(ab+bc+ca)+2(a+b+c)=766
2(250-a-b+300-b-c+216-a-c)+2(a+b+c)=766
1532-(a+b+c)=766
2(a+b+c)=766
a+b+c=383

Is this solution Helpfull? Yes (1) | No (1)  

pritam banerjee  (10 years ago)

jusr replace a by b b by c and reduce the eqtns a one variable stmnt

Is this solution Helpfull? Yes | No (1)  

chaitra l  (10 years ago)

i feel data is insufficient.can any 1 give me the solution with all steps????

Is this solution Helpfull? Yes | No (2)  

Am  (10 years ago)

a=34;
b=-50;
c=84;
a+b+c=68

Is this solution Helpfull? Yes | No (4)  

Deepali Chandak  (9 years ago)

Answer is 45.25

Is this solution Helpfull? Yes | No   

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