Direction : Study the table chart carefully and answer the questions given beside.
 
Person No. of days they worked Percentage of work done to complete the project
A 8 20%
B 3 10%
C 6 25%
D 15 30%
E 6 15%

Important for :
1
A and B started doing the work. After 10 days they both left, and C joined the work. He completed his part of work. Now the remaining work was completed by F in 16 days. In how many days can F complete whole work?
» Explain it
B
A does 20% work in 8 days.

So, 100% work in 100 ×  8  = 40 days
20

B does 10% work in 3 days
 
So, 100% work in 100 ×  3  = 30 days
10

1 day work of A and B together is:-
 
So,  1  +  1  =  7
40 30 120

So in 10 days they completed 7/12 part of the work

Now, C completed 25% =  1  of work
4

So now remaining work
=   1 – ( 7  +  1 )  =  1
12 4 6

F complete  1  work in 16 days,
6

So complete work in 96 days.

Hence, option (B) is correct.
 
2
G who can complete whole work in 30 days replaced A and did A’s part of work. He left and then B also worked for same number of days as G. If remaining work was completed by M who can do complete work in one-fourth the number of days in which E can complete the work, then in how many days was the whole work completed?
» Explain it
D
A’s part of work = 20% =  1
5

So, G did 1/5 of work and whole work in 30 days,
⇒  1  work in  1  × 30 = 6 days
5 5

Now, B also worked for 6 days.

B can complete 10% of work in 3 days.
So, B can complete the whole work in taken time 
=   100 ×  3  
10
=   30 days

So, in 6 days,
B completed  6  =  1  of work
30 5

Now, remaining work
=   1 –  ( 1  +  1 )  =  3
5 5 5

Now, E can complete 15% of work in 6 days. 
So, E can complete the whole work in taken time
=   100 ×  6  
15
=   40 days

M can complete the work in 1/4th of No. of days of E.
=    1  × 40
4
=   10 days.

So, M completed 3/5 work in taken time 
=    3  × 10 = 6 days
5

Hence, total number of days
=   6 + 6 + 6
=   18

Therefore, option D is correct.
 
3
If all people divides the work equally. In how many days will the work be completed this way?
» Explain it
B
people equally divided the work so each did 1/5 work now 
 
A does 1/5th work in 8 days 
 
B does 1/10th (10%) work in 3 days
⇒   1/5th of work in 6 days 

C does 1/4th (25%) work in 6 days
⇒   1/5th work in 4.8 days
 
D does 3/10th (30%) work in 15 days
⇒   1/5th work in 10 days 
 
E does 3/20th (15%) work in 6 days
⇒   1/5th work in 8 days 

Hence, total work completed in
=   8 + 4.8 + 6 + 10 + 8
=   36.8 days
 
Therefore, option B is correct.
 
4
P is 20% more efficient than B and Q is 60% more efficient than C. They worked together for 5 days and left the work, after which the remaining work was completed by D in ?
» Explain it
C
B can complete 10% of work in 3 days.
So, B can complete the whole work in
   100 ×  3  = 30 days
10


As P is 20% more efficient than B

⇒ P can complete the work in 25 days


C can complete 25% of work in 6 days.
So, C can complete the whole work in
   100 ×  6  = 24 days
25


As Q is 60% more efficient than B

⇒ Q can complete the work in 15 days


Now, P & Q worked for 5 days,
⇒  5  +  5  =  8
25 15 15

Remaining work = 1 –  8  =  7  
15 15


D can complete 30% of work in 15 days.
So, D can complete the whole work in
   100 ×  15  = 50 days
30


So, D does 7/15th of work in
   50 ×  7  = 23 1  days
15 3


Hence, option C is correct.

5
A shopkeeper can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the shopkeeper sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
» Explain it
C
Let us assume he buys n goods.
 
Total CP = 20n
 
Total SP = 2 + 4 + 6 + 8 ….n terms
 
Total SP should be at least 40% more than total CP
 
2 + 4 + 6 + 8 ….n terms ≥ 1.4 × 20 n
 
2 (1 + 2 + 3 + ….n terms) ≥ 28n
 
Sum of n – terms =  {n (n + 1)}
2

n (n + 1) ≥ 28n
 
n2 + n ≥ 28n
 
n2 – 27n ≥ 0
 
n ≥ 27
 
He should sell a minimum of 27 goods.

Hence, option (C) is correct.