Q : A and B can do a work together in 18 days. A is three times as efficient as B. In how many days can B alone complete the work?
(A) 60 days
(B) 72 days
(C) 54 days
(D) 64 days
Let's denote the work rate of A as "A" and the work rate of B as "B." We know that A is three times as efficient as B, so we can write:
A = 3B
Now, we also know that A and B can do a work together in 18 days. The work rate of A and B combined is the sum of their individual work rates, which can be represented as:
A + B
Since they complete the work in 18 days together, we can write:
(A + B) = 1/18
Now, we want to find how long it would take B alone to complete the work. Let's denote that time as "x" days. The work rate of B alone would be:
B (work rate of B alone) = 1/x
Now, we have two equations:
A = 3B
(A + B) = 1/18
We can substitute the value of A from the first equation into the second equation:
(3B + B) = 1/18
Combine like terms:
4B = 1/18
Now, isolate B by dividing both sides by 4:
B = (1/18) / 4
B = 1/72
So, B's work rate is 1/72 of the work per day. To find how many days B alone can complete the work, take the reciprocal of B's work rate:
x (number of days for B alone) = 1 / (1/72)
x = 72
Therefore, it would take B alone 72 days to complete the work.
A and B start moving from places X and Y and Y to X, respectively, at the same time on the same day. After crossing each other, A and B take
(A) 22
(B) 2
(C)
(D)
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman C, find in how many days B alone can do the work?
(A) 90 days
(B) 100 days
(C) 80 days
(D) 75 days
A can do
(A) 15 days
(B) 10 days
(C) 18 days
(D) 12 days
To do a certain work, the ratio of the efficiencies of A and B is 7: 5. Working together, they can complete the same work in
(A) 18 days
(B) 15 days
(C) 16 days
(D) 21 days
The respective ratio between the present ages of Rani and Moni is 6 : 7. If Moni is 4 years older than Rani, then what will be the respective ratio of the ages of Rani and Moni after 4 years?
(A) 4 : 3
(B) 7 : 8
(C) 3 : 4
(D) 3 : 5
The ratio of the monthly incomes of X and Y is 5: 4 and that of their monthly expenditures is 9: 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?
(A) 9 : 8
(B) 6 : 7
(C) 8 : 9
(D) 7 : 6
A, B and C invested capital in the ratio 5: 7: 4, the timing of their investments being in the ratio x : y : z. If their profits are distributed in the ratio 45: 42: 28, then x : y : z = ?
(A) 9 : 6 : 7
(B) 7 : 9 : 4
(C) 9 : 4 : 7
(D) 6 : 7 : 9
The radii of two right circular cylinders are in the ratio 3:2 and the ratio of their volumes is 27: 16. What is the ratio of their heights?
(A) 8:9
(B) 3:4
(C) 4:3
(D) 9:8
The monthly incomes of A and B are in the ratio 3 : 5 and the ratio of their savings is 2: 3. If the income of B is equal to three times the savings of A, then what is the ratio of the expenditures of A and B?
(A) 5:8
(B) 8:15
(C) 3:7
(D) 7:11
Get the Examsbook Prep App Today