Time and Distance and Time and work (UPSC) Part-II

Total Questions: 32

31. X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work? [2024-II]

(a) 6 hours 15 minutes
(b) 6 hours 30 minutes
(c) 6 hours 45 minutes
(d) 7 hours

Correct Answer: (c) 6 hours 45 minutes

Solution:X do more work / hour then y and z.
so, to get the work done in minimum possible time,
X have to do more number of hours.
∴ Working pattern would be.
X,(Y or Z), X, (Y or Z) . . .

X’s one hour work = 1/6 unit
Y’s one hour work = 1/8 unit

In 2 hour, amount of work finish = 1/6 + 1/8 = 4 + 3 / 24 = 7/24.

In 6 hour, work done = 3 × 7 / 24

Remains work = 1 - 3 × 7 / 24 = 3 / 24 = 1/8

X finish 1/8 work in 6 × 1/8 hours = 45 minutes.

∴ Total time required = 6 hours 45 minutes.

32. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [2024-II]

A certain amount was distributed among X, Y and Z.
Question:
Who received the least amount?

Statement–I:
X received $45\frac{4}{5}$ of what Y and Z together received.

Statement–II:
Y received $27\frac{2}{7}$ of what X and Z together received.

Which one of the following is correct in respect of the above
Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together

Correct Answer: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Solution:S₁ : x = 4/5 (y + z) ⇒ 5x = 4 (y + z)

S₂ : y = 2/7 (x + z) ⇒ 7y = 2 (x + z)

From S₁ and S₂, By replacing y from two equations.

5x = 4 ( 2/7 (x + z) + z )

35x = 8x + 36z

27x = 36z

3x = 4z

∴ x > z

Again, by Replacing x from two equation.

7y = 2 ( 4/5 (y + z) + z )

35y = 8y + 18z

27y = 18z ⇒ 3y = 2z

∴ 3x = 6y = 4z

Hence, y < z < x.

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Time and Distance and Time and work (UPSC) Part-II

32. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [2024-II]

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