Question

Two worker's A and B working together
completed a job in 15/2 days. If A worked
twice as efficiently as he actually did and B

worked thrice as efficiently as he actually
did, the work would have been completed in
10/3 days. how many days B required to
complete the job?​

Answer 1

Given :-

● A and B working together completed a job in 15/2 days.

● If A worked twice as efficiently he actually did, the work would have been completed in 10/3 days.

Solution :-

Let the amount of work needed to complete a job be x

Now,

Let ' a ' be the amount of work done by worker A in one day

Let ' b ' be the amount of work done by worker B in one day

Therefore,

According to the question,

15a/2 + 15b/2 = x eq( 1 )

Now,

( 10a/3 ) 2 + ( 10b/3 )3 = x. eq( 2 )

Since, Both eqn are equal to x

Therefore,

15a/2 + 15b/2 = ( 10a/3)2 + ( 10b/3)3

15a/2 + 15b/2= 20a/3 + 10b

15a/2- 20a/3 = 10b - 15b/2

● By taking LCM both side

45a - 40a/6 = 20b - 15b/2

5a/6 = 5b/2

5a = 5b/2 * 6

5a = 15b

a = 15b/5

a = 3b

Now,

● Subsitute the value of a in eq( 1 )

Therefore,

15(3b)/2 + 15b/2 = x

45b/2 + 15b/2 = x

45b + 15b / 2 = x

60b/2 = x

30b = x

Hence, Worker B can do the same job in 30days $.$

Answer 2

Answer:

$\huge \underline \mathfrak \red{Given}$

★ A and B working together completed a job in 15/2 days.

★ If A worked twice as efficiently he actually did, the work would have been completed in 10/3 days.

$\huge \underline \mathfrak \red{Solution}$

Let the amount of work needed to complete a job be x

Now,

Let ' a ' be the amount of work done by worker A in one day

Let ' b ' be the amount of work done by worker B in one day

Therefore,

According to the question,

15a/2 + 15b/2 = x eq( 1 )

Now,

( 10a/3 ) 2 + ( 10b/3 )3 = x. eq( 2 )

Since, Both eqn are equal to x

Therefore,

15a/2 + 15b/2 = ( 10a/3)2 + ( 10b/3)3

15a/2 + 15b/2= 20a/3 + 10b

15a/2- 20a/3 = 10b - 15b/2

▶By taking LCM both side

45a - 40a/6 = 20b - 15b/2

5a/6 = 5b/2

5a = 5b/2 * 6

5a = 15b

a = 15b/5

a = 3b

Now,

▶ Subsitute the value of a in eq( 1 )

Therefore,

15(3b)/2 + 15b/2 = x

45b/2 + 15b/2 = x

45b + 15b / 2 = x

60b/2 = x

30b = x

Hence, Worker B can do the same job in 30 days