A takes 10 days less than the time taken by B to finish a piece of work, if both A and B together finish a work in 12 days. Find the time taken by B to finish the work.

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31 Jul 2013 Problem A takes 10 days less than the time taken by B to finish a piece of work, if both A and B together finish a work in 12 days. Find the time taken by B to finish the work.: OPtion
1) 1
2) 11
3) 15
4) 25
5) 30
6) 20
7) 35
8) 40
9) 50
10)None of these; Correct Option: 5 Best Solution (31)

vigneshwari 11 years AGO

Let the time taken by B be X days.
Then the time taken by A is X-10 days.
B's 1 day's work = 1/X and A's 1 day work = 1/X-10.
Time taken by A and B together = 12 days.
Then A+B 's 1 day's work = 1/12
Therefore, 1/12 = 1/X + 1/X-10
=> X^2 - 34X + 120 = 0
=> (X-30)(X-4) = 0
That is X is either 30 or 4.
4 is not possible and hence 30 is the answer.

Like? Yes (39) | No (7)

Aditi Gupta 11 years AGO

let b takes x days
then A will take x-10 days
then when they work together
1/(x-10) + 1/x = 1/12
after solving
x=30 or x=4
so we reject x=4 since we cant subtract 10 days from it for A s.
x=30 ans

Like? Yes (18) | No (2)

ravi singh 11 years AGO

let A takes x days then B take (x+10) days as given in question,

1/x + 1/(x+10) = 1/12

by solving this we get x= -6, 20

since days r not negative hence x=20

therefore work done by B=20+10=30

Like? Yes (17) | No (5)

Deepak Sharma 11 years AGO

let B finish that work in x days
then A will finish that work in x-10 days
so A do 1/x-10 work nd B do 1/x work.
and both together do 1/12 work
then, 1/x + 1/x-10 = 1/12
after solving this x=30days

Like? Yes (11) | No (4)

sajjan kumar 11 years AGO

1/30 + 1/20 =1/12

Like? Yes (11) | No (6)

amit kumar burnwal 11 years AGO

let B takes d days to finish a piece of work.
so, a takes (d-10) to finish a piece of work.
so,by question,
1/(d-10)+ 1/d =1/12
d^2-10d-24d+120=0
(d-30)(d-4)=0
d=4 or 30
4 day is not possible because A takes 10 days less than the time taken by B to finish the work .
so,
ans: 30 days

Like? Yes (7) | No (3)

ABHISHEK KUMAR MISHRA 11 years AGO

let B takes x days
so to the question
for 1 day both part of work=1/x + 1/x-10
so 1/x + 1/x-10 = 1/12
x=30,4
but here x=30

Like? Yes (6) | No (4)

krishnapriya 11 years AGO

Let B alone finish the work =x days
A finish the work=(x-10) days
A's one day work=1/(x-10)
B's one days work=1/x
1/(x-10)+1/x=1/12
solving the above
we get x=4 or x=30
therefore x=30

Like? Yes (2) | No (1)

Ish Mishra 11 years AGO

Let B take "x" days to finish "y" work.
Then ,A takes "x-10" days to finish "y" work.

Work of B in 1 day = y/x
Work of A in 1 day=y/(x-10)

Given both complete work in 12 days:

[(y/x)+y/(x-10)]*12 = y
Solving this:
x=30

Like? Yes (2) | No (1)

Gaurav Sharma 11 years AGO

let time taken by B =x
and that taken by A=x-10
now work done by B in one day=(1/x)
and that by A=(1/(x-10))
work done by them together in one day=(1/x)+(1/(x-10))
given work done by them together in 12 days
now one day work by both of them=1/12
now equating both the equations
(1/x)+(1/(x-10))=1/12
on solving we have x=4 and 30
so we can reject 4 and taking x=30 which is time taken by B to finish the work.

Like? Yes (3) | No (2)

Bingumalla Abinay 11 years AGO

let work by B be x and then A becomes x-10
for 1 day their respective work's are 1/x,1/x-10
adding both we get 1/x+1/(x-10)=1/12
solving x=30 or 4
as 4 is not possible 30 is answer

Like? Yes (1) | No

Roopam Jain 11 years AGO

1/(x-10) + 1/x = 1/12

On solving x = 30 , 4

Like? Yes (1) | No

divya arora 11 years AGO

let time taken by b=1/b;
time taken by a=1/(b-10)
1/b+1/(b-10)=1/12
b^2-34b-120=0
solving b=30

Like? Yes (1) | No

mandira kundu 11 years AGO

let B takes x days,then A takes x-10 days to finish the whole work.
so B does 1/x of work and A 1/x-10 in 1day.
then total work done in 1day=1/x+1/x-10
so,1/x+1/x-10=1/12
solving x=30.

Like? Yes (3) | No (2)

Chandni Maurya 11 years AGO

Ans=(5). 30
let B takes time = x days
& A takes time = y days
time taken by together A & B = 12
=> x.y/(x+y) = 12 --- (1).
according to question,
y=x-10
put y in (1),
=> x(x-10)/[x+(x-10)] = 12
=> (x^2-10x)/(2x-10) = 12
=> x^2 -10x = 24x-120
=> x^2-34x+120 = 0
=> x^2-30x-4x+120=0
=> (x-4)(x-30) = 0
=> x=4 & x=30
here x can't be equal to 4.
( as,time taken by A will be,
=> 4-10=-6, which is not possible)
=> x= 30 (Ans=(5).30)

Like? Yes (2) | No (1)

sanjay singh 11 years AGO

let B finish work alone in x days
A finish in x-10 days
in 12 days they complete work together
12/(x-10) + 12/x =1
solving we get x=4 or 30
neglecting 4 ,the option is 30
so option 5 is correct

Like? Yes (1) | No

niraj kumar 11 years AGO

let us suppose B can compelete the work in x day
fraction of work in 1 day by b=1/x
so A can COMPLETE in x-10day
fraction of work by A in 1 day=1/x-10
now they both do 1/12 fraction of work
therefore,
1/x+1/x-10 =1/12
solve for x we get x=4,30
as both do it in 12 day
so neglect 4 we get 30 approprite ans

Like? Yes (3) | No (2)

saranya 11 years AGO

let no of days B work is x
then no of days A work be y=x-10
then a,b work togather is xy/x+y=12
then x(x-10)/2x-10=12
on solving we get 30,4
4 cannot be ans bcoz on applying 4 on a work then it bcom -6..
so 30 is answer.

Like? Yes (3) | No (2)

Tushar Gupta 11 years AGO

Let B take x days to complete the work.
So, A takes x-10 days to complete the same work.

Amount of work done by A in one day = 1/(x-10)
Amount of work done by B in one day = 1/x

When they work together,
A+B=12

In 1 day, 1/A + 1/B = 1/12

=> 1/x-10 + 1/x = 1/12

On solving, x= 30 or x=4
x cannot be 4 since that would mean A does the work in -6 days, which is not possible.

So, x = 30, i.e. the no. of days B alone can do the work.

Like? Yes (2) | No (1)

Amit kumar 11 years AGO

let A finish the work in x days
acoording to ques B finish the work x+10 days
so,1/x+1/x+10=1/12
after solving
x=20
the B finish the work =x+10=20+10=30ans

Like? Yes (2) | No (2)

jitendra sharma 11 years AGO

if B takes x days than A takes x-10 days;
1/x+1/x-10=1/12
value of x from above equation
4,30;
but 4 is not satisfy bcoz A's time =4-10=-6;
which is wrong
so,30 is correct answer..

Like? Yes (1) | No (1)

Bagmita Chanda 11 years AGO

ler b takes x days to complete a work
so a takes x-10 days
in 1 day a & b togather can do = (1/x)+(1/(x-10))
again in 12 days they can complete a task
so in 1 day they can complete 1/12 part of the task

so (1/x)+(1/(x-10))=1/12
=> x=30

Like? Yes (2) | No (2)

Saloni Singh 11 years AGO

Let B finish the work in b days
so A will finish the work in b-10 days
A+B's 1 day work=1/12
B's 1 day work=1/b
A's 1 day work=1/(b-10)
so,
(1/b)+(1/b-10)=1/12
=>b^2-34b+120=0
Now,using the formulae for roots of quadratic equatn,
b=[34+(1156-480)^1/2]/2
or
b=[34-(1156-480)^1/2]/2
so we get b=4 or 30days
considering the fact that A takes 10 days less than B, we conclude that B does the work in 30 days.

Like? Yes (1) | No (1)

Balakrishnan M 11 years AGO

Let B finish a piece of work in x days.
then A takes to finish the same work is x-10 days.
A's work done by 1 day = 1/(x-10)
B's work done by 1 day = 1/(x)
Both A and B working together, their work done by 1 day = (1/(x-10))+(1/x)
= (2x-10)/(x^2-10x)
Both A and B together can finish a work in
= (x^2-10x)/(2x-10)days.
Given that,
both A and B together finish a work in 12 days.
==> (x^2-10x)/(2x-10)=12
==> x^2-10x=24x-120
==> x^2-34x+120=0
==> (x-30)(x-4)=0
==> x=30 or 4
Then B can finish the work in 30 days.

Like? Yes (1) | No (1)

divyang 11 years AGO