Quiz-1

Ratio of efficiency of Shush and Komal = 1:7/4 = 4:7
As the time taken is inversely proportional to efficiency, therefore, if Komal takes 7x days to complete work, Asha will take 4x days.
Therefore 1/7x + 1/4x = 1/7 => (4+7)/28x = 1/7
=> 28x = 11 × 7
Therefore x = {(11×7)/28} = 11/4
Shush will complete the work in 4x = 4 (11/4) = 11 days.

Anil and Babu can do a job in 8 days
Combined efficiency of Anil + Babu = 100/8 = 12.5% ……………………………………(1)
Similarly, combined efficiency of Babu + Charan = 100/12 = 8.33%……………………..(2)
Similarly, combined efficiency of Anil + Babu + Charan = 100/6 = 16.66%……………..(3)
So now, if we want to calculate the efficiency of Anil and Charan together, we need to first calculate the individual efficiency of Anil and Charan.
So we first deduct equation 1 from equation 3 to get efficiency of Charan. Then we deduct equation 2 from equation 3 we will get efficiency of Anil.
Let’s calculate the efficiency of Charan = (Anil + Babu + Charan) – (Anil + Babu) = 16.66 – 12.5 = 4.16%
In the same way, we calculate the efficiency of Anil = 16.66 – 8.33 = 8.33%
So, combined efficiency of Anil and Charan = 8.33% + 4.16% ˜ 12.5%
They need = 100/12.5 = 8 days.
So they can complete the job in 8 days.Anil and Babu can do a job in 8 days
Combined efficiency of Anil + Babu = 100/8 = 12.5% ……………………………………(1)
Similarly, combined efficiency of Babu + Charan = 100/12 = 8.33%……………………..(2)
Similarly, combined efficiency of Anil + Babu + Charan = 100/6 = 16.66%……………..(3)
So now, if we want to calculate the efficiency of Anil and Charan together, we need to first calculate the individual efficiency of Anil and Charan.
So we first deduct equation 1 from equation 3 to get efficiency of Charan. Then we deduct equation 2 from equation 3 we will get efficiency of Anil.
Let’s calculate the efficiency of Charan = (Anil + Babu + Charan) – (Anil + Babu) = 16.66 – 12.5 = 4.16%
In the same way, we calculate the efficiency of Anil = 16.66 – 8.33 = 8.33%
So, combined efficiency of Anil and Charan = 8.33% + 4.16% ˜ 12.5%
They need = 100/12.5 = 8 days.
So they can complete the job in 8 days.

Ratio of times taken by A and B = 1 : 2.
The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.
If difference of time is 1 day, B takes 2 days.
If difference of time is 30 days, B takes 2 x 30 = 60 days.
So, A takes 30 days to do the work.
A's 1 day's work = 1/30
B's 1 day's work = 1/60
(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20
A and B together can do the work in 20 days.

Explanation:

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.

(A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work = (1/4-1/12)=3-1/12=1/6.
So B alone can complete the work in 6 days

Efficiency of A and B = 1/20 per day = 5% per day ________________1
Efficiency of B and C = 1/30 per day = 3.33% per day______________2
Efficiency of C and A = 1/30 per day = 3.33% per day______________3
Taking equation 2 and 3 together
B + C = 3.33% and C + A = 3.33%
C and 3.33% will be removed. Hence A = B
Efficiency of A = B = 5%/2 = 2.5% = 1/40
Efficiency of C = 3.33% - 2.5% = 0.833% = 1/120
A can do the job in 40 days and C can do the job in 120 days he they work alone.
Ratio of number of days in which A and C can complete the job 1:3.