DUY Q. 41 : If each woman type 12 papers a day then 9 women required to type full book in 15 days. If the same book is typed by 18 women typing 15 paper a day how many days are required to type the book? (1) 8 (2) 10 (3) 12 2. (4 6 6 8 10
Answers
Answer:
(1)Given 6 typists typing 8 hours a day (at equal speed) take 20 days to complete a manuscript.
We have to find the number of typists to be employed if each typist works for 5 hours a day to complete the work in 12 days.
When number of typists=6
The number of working hours a day=8 hours
And number of days to complete the work=20 days
⇒ The total work will be =number of typists× number of hours ×number of days {because Work =time ×number of people doing the work}
Now on putting the given values we get-
⇒ The total work=6×8×20 --- (i)
Now let the number of typists be x then the number of working hours a day =5 hours
And the number of days to complete the work =12 days
⇒ The total work will be =number of typists× number of hours ×number of days {because Work =time ×number of people doing the work}
On putting the given values, we get-
⇒ The total work=x×5×12 -- (ii)
Now since the work is the same then on equating eq. (i) and (ii), we get-
⇒x×5×12=6×8×20
On re-arranging, we get-
⇒x=6×8×205×12
On simplifying, we get-
⇒ x=96060
On division, we get-
⇒ x=16
Since there are already 6 typists employed then the number of typist to be employed=16−6
On solving, we get-
Answer-The number of typists to be employed=10
(2)
a. Given, 2 men and 8 women can finish a piece of work in 15 days.
Then we can write,
In 15 days, the number of men and women required=2 men +8 women
Then in one day, the number of men and women required=15 (2 men +8 women)
On solving, we get-
In one day, the number of men and women required= 30 men +120 women-- (i)
Now, it is given that8 men and 16 women can finish the same work in 6 days.
So we can write,
In one day, the number of men and women required=6 (8 men +16 women)
On solving, we get-
In one day, the number of men and women required=48 men +96 women-- (ii)
We have to find the number of women equivalent to 3 men according to the amount of work done.
On equating eq. (i) and (ii), we get-
⇒ 30 Men +120 women=48 men +96 women
On taking the value of number of men on one side and value of number of women on the other side, we get-
⇒ 120Women-96 women =48 men -30 men
On solving, we get-
⇒24 Women=18 men
Then 1 men=2418 women
On solving, we get-
⇒ 1 Men=43 women
Then 3 men=43×3 women
On solving we get-
Answer-3 Men=4 women
b. Given, 2 men and 8 women can finish a piece of work in 15 days. It is given that8 men and 16 women can finish the same work in 6 days.
Let one man’s one day’s work=x and one woman’s one day work =y
Then we get-
⇒2x+8y=115 -- (i)
And 8x+16y=16 -- (ii)
On multiplying 2 in eq. (i) and subtracting eq. (ii) from eq. (i), we get-
⇒−4x=215−16
On solving, we get-
⇒4x=16−215
On taking LCM we get,
⇒4x=5−430=130
On further solving, we get-
⇒x=1120
On substituting this value in eq. (i), we get-
⇒2120+8y=115
On solving, we get-
⇒2+960y120=115
On further solving, we get-
⇒2+960y=8
⇒960y=6
⇒y=1160
The work done by 9 men and 4 women to complete the same work=9x+4y
On putting value of x and y we get,
The work done by 9 men and 4 women to complete the same work=9120+4160=110
The time taken by 9 men and 4 women to complete the same work = 10 days.
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