Quiz 5

Question 1

Anuj, Bibhuti and Chandu can lay 432 m of wires together in 8 days. In a day, Chandu can lay as many more meters of wire than Bibhuti as Bibhuti can lay more than Anuj. Chandu’s 5 days of work is equivalent to Anuj’s 7 days of work. How many meters of wire can Anuj alone lay in a day?

9

13.43%

15

55.22%

18

20.9%

21

10.45%

  • PrepInsta Explanation
  • User Explanation

On an average, 543543 = 18 m will be laid by each which as per question should be the length Bibhuti can lay in a day.
Therefore, Anuj = 18 – x ; Chandu = 18 + x
Given,
7 * (18 – x) = 5 * (18 + x)
126 – 7x = 90 + 5x
=> 36 = 12x
=> x = 3
Therefore, Anuj in a day = 18 – 3 = 15 m

The question is How many meters of wire can Anuj alone lay in a day?

Hence, the answer is 15 m.

Question 2

A certain number of pages need to be typed. A, B and C are assigned to do this job. However, C leaves after 4 days when 40% of the job was complete. In this way, it takes 13 days to finish the job. Also, B can type twice as fast as A. How much would the fastest worker take to type the entire set of pages alone?

22.5 days

52.38%

20 days

25.4%

30 days

15.87%

40days

6.35%

  • PrepInsta Explanation
  • User Explanation

A and B take 9 days to complete the remaining 60% of the job.
Therefore, in one day A and B can complete – 609609 = 203203 of the job
Since B is twice as fast as A,
B can finish = 203203 * 2323 = 409409 of the job in a day
A can finish = 203203 * 1313 = 209209 of the job in a day
In the first 4 days. A and B would have finished = 203203 * 4 = 803803 of the job
Therefore, C would have finished = 40 % - 803803 = 403403 of the job in 4 days
So, in a day C finishes = 40124012 of the job
Thus, clearly B is the fastest among the three workers

The question is How much would the fastest worker take to type the entire set of pages alone?

Hence, the answer is 22.5 days.

Question 3

A, B and C are to make 100 toys. In a day, they can together make 25 toys. A starts to work alone and makes 32 toys in some days. A then leaves and B and C works to make the remaining toys. It takes 8 days overall to make the 100 toys. How many days will it take for A to make 256 toys alone?

16

16.36%

32

63.64%

64

12.73%

30

7.27%

  • PrepInsta Explanation
  • User Explanation

A, B and C together could make 100 toys in 1002510025 = 4 days
i.e. A + B + C => 4 days
Total time taken when first A worked then B + C worked -> 8 days (i.e. 2 x 4)
Hence, it is as if A and (B+C) worked alternatively for 4 days each to complete the 100 days
So, A can make 32 toys in 4 days => In a day, A can make = 324324 = 8 toys/day
To make 256 toys, A will take = 25682568 = 32 days

The question is How many days will it take for A to make 256 toys alone?

Hence, the answer is 32 days.

Question 4

Amar, Akbar, and Anthony set out to complete a work. Anthony being the eldest would take 1 day less than Amar if he were to complete the work alone. All three together could complete the work in a day. However, Anthony was kidnapped by Shakal. Amar and Akbar began the work in his absence. After a day, Amar was also kidnapped. Akbar took 3 more days to finish the work. How many portions of the work Anthony could do in a day?

2/3

29.41%

1/6

25.49%

1/2

33.33%

1/3

11.76%

  • PrepInsta Explanation
  • User Explanation

Let Amar take x days and Akbar takes y days to finish the work. So, Anthony would take x-1 days to complete the work alone.
Therefore, as per question,
1x1x + 1(x−1)1(x−1) + 1y1y = 1 …………………(1)
Also given, (1x1x + 1y1y + 3y3y) = 1
=> 1x1x + 4y4y = 1
=> (1y1y = 1414 + 14x14x = 1 ………………………(2)
Putting in equation (1),
=> 1x1x + 1(x−1)1(x−1) + 1414 - 14x14x = 1
=> 1x1x + 1(x−1)1(x−1) - 14x14x = 3434
Now using option analysis,
a) Work done by Anthony in 1 day = 1(x−1)1(x−1) = 2323 =) 3 = 2x - 2 =) x = 5252 = 2.5
L.H.S of (3) => 12.512.5 + 11.511.5 - 110110 = 0.4 + 0.66 – 0.1 ≠ 0.75
b) 1(x−1)1(x−1) = 1616 =) x = 7 L.H.S of (3) = 1717 + 1616 - 128128 ≠ 3434
c) 1(x−1)1(x−1) = 1212 =) x = 3 L.H.S of (3) = 1313 + 1212 - 112112 = (4+6–1)12(4+6–1)12 = 912912 = 3434

The question is How much portion of the work Anthony could do in a day?

Hence, the answer is "1/2".

Question 5

It’s the year 2025 and iphone16 has just been launched. Apple has claimed that it is the best iPhone they have created so far. It’s 4 charging inlets have completely revolutionized the mobile market. If the only top and bottom inlets are used, it takes 20 mins to fully charge. If the right, left and bottom inlet are used, it takes 15 mins to fully charge. If top, left and right inlets are used, it takes 12 mins to charge. What is the fastest possible time in which the iphone16 can be fully charged?

12 min

24.14%

8 min

27.59%

11  min

5.17%

10 min

43.1%

  • PrepInsta Explanation
  • User Explanation

Obviously, if all the 4 inlets are used, the iPhone will be recharged in the fastest possible time.
Let, Time taken by Top, Left, Right, and Bottom inlet to individually charge the phone be represented by A, B, C, and D respectively.
Given,
1A1A + 1D1D = 120120
1B1B + 1C1C + 1D1D = 115115
1A1A + 1B1B + 1C1C = 112112
On adding all 3,
=> 2 * (1A1A + 1B1B + 1C1C + 1D1D) = 112112 + 115115 + 112112 = (15+20+25)300(15+20+25)300 = 1515
=> 1A1A + 1B1B + 1C1C + 1D1D = 110110
Therefore, all 4 together will take 10 minutes to fully charge the iphone.

The question is What is the fastest possible time in which the iphone16 can be fully charged?

Hence, the answer is 10 min.

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