Top 100 Aptitude Questions and Answers for Competitive Exams
Aptitude Questions and Answers
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
Correct Answer : B
Explanation :
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 $$5{4\over 9}$$ hours and 9 hours, respectively, to reach their respective destinations. If the speed of A is 33 km/h, then the speed (in km/h) of B is:
(A) 22
(B) 2
(C) $$25{2\over 3}$$
(D) $$24{1\over 3}$$
Correct Answer : C
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
Correct Answer : A
A can do $$1\over 3$$ of a work in 30 days. B can do $$2\over 5$$ of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:
(A) 15 days
(B) 10 days
(C) 18 days
(D) 12 days
Correct Answer : D
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 $$17{1\over 2}$$ days. A alone will complete 60% of the same work in:
(A) 18 days
(B) 15 days
(C) 16 days
(D) 21 days
Correct Answer : A
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
Correct Answer : B
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
Correct Answer : A
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
Correct Answer : A
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
Correct Answer : B
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
Correct Answer : B
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Vikram Singh
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