5 Challenges on 05.12.14

( Time & Work)

1.A and B together can do a piece of work in 12 days ,while B alone can finish it in 30 days. A alone can

finish the work in

1)15days 2)18 days 3)20 days 4)25 days 5) None of these

Solution : (3).

(A+B)’ s 1 day’s work = 1/12

B’s 1 day’s work = 1/30

Therefore A’s 1 days’s work = 1/12 – 1/30

= 5-2 / 60 = 1/20

2.A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In

what time can A alone do it?

1)80 days 2) 100 days 3)120 days 4)150 days 5)None of these

Solution : (3).

( A+B)’s 1 days’s work = 1/72

( B+C)’s 1 day’s work = 1/120

(A+C)’s 1 day’s work = 1/90

2((A+B+C)’s 1 day’s work

= 1/72 + 1/120 + 1/90

Therefore ( A+B+C)’s 1 day’s work

= (5+3+4) / (360 x 2) = (12/360 x 2 ) = 1/60

Therefore A’s 1 days’s work = (A+B+C)’s 1 day’s work – ( B+C)’s 1 day’s work

= 1/60 – 1/120 = 2 – 1 /120 = 1/120

Therefore A alone can finish the work in 120 days.

3.’A’can do a piece of work in x days and B can do the same work 3x days. To finish the work together

they take 12 days. What is the value of x ?

1)8 2)10 3)12 4)16 5)None of these

Solution : (4).

A’s 1 day’s work A = 1/x

B’s 1 day’s work B = 1/3x

( A+B)’s 1 day’s work

= 1/x + 1/3x = 4/3x

And given one day work of both A and B = 1/12

= 4/3x = 1/12 = 3x = 48 = x = 16

4.A can do a piece of work in 10 days and B in 20 days . They begin together but A leaves 2 days before

the completion of the work. The whole work will be done in

1)8 days 2) 7 2/3 3)7 days 4) 6 days 5)None of these

Solution : (1).

Here, a = 10 , b = 20 and x = 2

Therefore required time = ( a + x) *b / (a + b)

= (10 + 2) *20 / 30 = 8 days

5.A and B can complete a job in 24 days working together. A alone can complete it in 32 days. Both of

them worked together for 8 days and then A left. The number of days B will take to complete the

remaining job is

1)16 2)32 3)64 4)128 5)None of these

Solution : (3).

Let B will take x days to complete the remaining job .

According to the question,

1/A + 1/B = 1/24 and 1/A = 1/32

Therefore 1/B = 1/24 – 1/32 = 1/96 = B = 96 days

According to the question,

8 ( 1/A + 1/B ) + x * 1/B = 1

= 8 x 1/24 + x/96 = 1

= 1/3 + x/96 = 1

x/96 = 1 – 1/3

therefore x = 2*96 /3 = 64

Hence, B complete the remaining job in 64 days.