Direction: Study the data carefully and answer the question given beside:
 
The 1st graph shows the percentage of work done in one day by five different boys and the 2nd graph shows the number of days taken by five different girls to do the same work.



1
If Amulya starts the work alone and after 2 days Aadhya joins him and after 1 day later Aarushi joins them, then, in how many days will the whole work be completed?
 
» Explain it
B
Anmol's efficiency is 12.5% so he can do the work in 100/ 12.5 = 8 days
 
Akash's efficiency is 8.33% so he can do the work in 100/ 8.33 = 12 days
 
Amulya's efficiency is  16.16% so he can do the work in 100/ 16.67 = 6 days
 
Akshat's efficiency is 6.67% so he can do the work in 100/ 6.67 = 15 days
 
Akhil's efficiency is 10% so he can do the work in 100/10 = 10 days

According to the question
Let the whole work will be completed in x days

x  +  (x – 2)  +  (x – 3)  = 1
6 12 18

(6x + 3x – 6 + 2x – 6)  = 1
36

11x – 12 = 36

11x = 36 + 12

11x = 48

x =  48  = 4 4  days
11 11

Hence, option B is correct.
2
Akshat’s efficiency is approximately how much percentage less than Anju’s efficiency?
» Explain it
C
Anmol's efficiency is 12.5% so he can do the work in 100/ 12.5 = 8 days
 
Akash's efficiency is 8.33% so he can do the work in 100/ 8.33 = 12 days
 
Amulya's efficiency is 12.5% so he can do the work in 100/ 16.67 = 6 days
 
Akshat's efficiency is 6.67% so he can do the work in 100/ 6.67 = 15 days
 
Akhil's efficiency is 10% so he can do the work in 100/ 10 = 10 days

Akshat's efficiency =  1
15

Anju's efficiency  =  1
9

less % = 
( 1  –  1 )
9 15
 × 100
1
9

6  × 9 × 100 = 40%
135

Hence, option C is correct.
3
Akshat started the work alone. Since he did not work with his actual efficiency, after 6 days he found that he had done only 30% of the work. If he wants to complete the work on time, by how much (percentage) should he increase his actual efficiency?
» Explain it
A
Anmol's efficiency is 12.5% so he can do the work in 100/ 12.5 = 8 days
 
Akash's efficiency is 8.33% so he can do the work in 100/ 8.33 = 12 days
 
Amulya's efficiency is 16.67% so he can do the work in 100/ 16.67 = 6 days
 
Akshat's efficiency is 6.67% so he can do the work in 100/ 6.67 = 15 days
 
Akhil's efficiency is 10% so he can do the work in 100/ 10 = 10 days

Let total work = 90

1 day's work =  90  = 6
15

6 day's work = 6 × 6 = 36

But he did = 90 × 30% = 27

In the remaining days (15 – 6) = 9 days he needs to complete (90 – 27) = 63 work

1 day's work =  63  = 7
9

Increased efficiency =  (7 – 6)  × 100
6

= 16 2 %
3

Hence, option A is correct.
4
Anmol and Akhil start working together and after 3 days Anmol leaves the work and Ananya joins him and completes the work. If instead of Ananya, Aishwarya would have joined, find the difference between the number of days taken in both cases.
» Explain it
B
Anmol's efficiency is 12.5% so he can do the work in 100/ 12.5 = 8 days
 
Akash's efficiency is 8.33% so he can do the work in 100/ 8.33 = 12 days
 
Amulya's efficiency is  16.67% so he can do the work in 100/ 16.67 = 6 days
 
Akshat's efficiency is 6.67% so he can do the work in 100/ 6.67 = 15 days
 
Akhil's efficiency is 10% so he can do the work in 100/ 10 = 10 days

Anmol's and Akhil's 1 day work =  1  +  1
8 10

Anmol's and Akhil's 3 day work =  ( 1  +  1 )  × 3
8 10

(5 + 4)  × 3 =  27
40 40

Remaining work = 1 –  27  =  13
40 40

Ananya's and Akhil's 1 day work =  1  +  1
16 10

Time to complete the work =  13  ÷  ( 1  +  1 )
40 16 10

13  ÷  13  = 2 days
40 80

Instead of Ananya, Aishwariya had joined,

Aishwariya's and Akhil's 1 day work =  1  +  1
10 10

Time to complete the work =  13  ÷  ( 1  +  1 )
40 10 10

13  ÷  1  =  13 days
40 5 8

Difference = 2 –  13  =  3
8 8

Hence, option B is correct.
5
What is the ratio of the number of days required if Aishwarya and Anmol work together to the number of days required if Akash and Arushi work together?
» Explain it
E
Anmol's efficiency is 12.5% so he can do the work in 100/ 12.5 = 8 days
 
Akash's efficiency is 8.33% so he can do the work in 100/ 8.33 = 12 days
 
Amulya's efficiency is 16.67% so he can do the work in 100/ 16.67 = 6 days
 
Akshat's efficiency is 6.67% so he can do the work in 100/ 6.67 = 15 days
 
Akhil's efficiency is 10% so he can do the work in 100/ 10 = 10 days

Aishwariya and Anmol can do the work =  1
1  +  1
  10 8

9  =  40 days
(9/40) 9

Akash and Arushi can do the work =  1
1  +  1
  18 12

1  =  36 days
(5/36) 5

Ratio =  40 : 36  = 50 : 81
9 5

Hence, option E is correct.