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A tunnel of length 360 m is to be constructed. As per the plan, the team has to complete the tunnelling within a specified period of time. For the first four days, the tunnelling was done according to the plan. However, it was found that the resources were being underutilized. It was then decided that the rate of tunnelling should be increased and then they started tunnelling 15 m more than their everyday plan. Therefore, a day before the planned date they had tunnelled to a length of 380 m. How many meters of tunnelling was planned for each day?
- a)48 m
- b)40 m
- c)36 m
- d)38 m
Correct answer is option 'B'. Can you explain this answer?
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A tunnel of length 360 m is to be constructed. As per the plan, the te...
Let, the per day tunnelling plan was ‘x’ meter and the tunnelling of 360 m was to be completed in ‘y’ day.
Therefore, xy = 360----(i)
Now, as per plan tunneling was done for four days and then rate of tunnelling was increased to
(x + 15) for (y - 4) days. One day before the planned date they have tunnelled 380 m.
∴ Number of days when the tunnelling was done at increased rate is
= (y – 4 - 1) = (y - 5) days
According to the statement given the following situations can be inferred
∴ 4x + (y - 5) (x + 15) = 380
⇒ 4x + xy + 15y – 5x – 75 = 380
⇒ 4x + 15y – 5x = 380 + 75 – xy
⇒ 15y – x = 380 + 75 – 360
⇒ 15y – x = 95 ----(ii)
Putting y value from eq (i) in eq (ii) we get
⇒ x2 + 95x – 5400 = 0
On solving the above quadratic equation, we get
⇒ x = 40 m
Therefore, xy = 360----(i)
Now, as per plan tunneling was done for four days and then rate of tunnelling was increased to
(x + 15) for (y - 4) days. One day before the planned date they have tunnelled 380 m.
∴ Number of days when the tunnelling was done at increased rate is
= (y – 4 - 1) = (y - 5) days
According to the statement given the following situations can be inferred
∴ 4x + (y - 5) (x + 15) = 380
⇒ 4x + xy + 15y – 5x – 75 = 380
⇒ 4x + 15y – 5x = 380 + 75 – xy
⇒ 15y – x = 380 + 75 – 360
⇒ 15y – x = 95 ----(ii)
Putting y value from eq (i) in eq (ii) we get
⇒ x2 + 95x – 5400 = 0
On solving the above quadratic equation, we get
⇒ x = 40 m
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A tunnel of length 360 m is to be constructed. As per the plan, the team has to completethe tunnellingwithin a specified period of time. For the first four days, the tunnelling was done according to the plan. However, it was found that the resources were being underutilized. It was then decided that the rate of tunnelling should be increased and then they started tunnelling 15 m more than their everyday plan. Therefore, a day before the planned date they had tunnelled to a length of 380 m. How many meters of tunnelling was planned for each day?a)48 mb)40 mc)36 md)38 mCorrect answer is option 'B'. Can you explain this answer?
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A tunnel of length 360 m is to be constructed. As per the plan, the team has to completethe tunnellingwithin a specified period of time. For the first four days, the tunnelling was done according to the plan. However, it was found that the resources were being underutilized. It was then decided that the rate of tunnelling should be increased and then they started tunnelling 15 m more than their everyday plan. Therefore, a day before the planned date they had tunnelled to a length of 380 m. How many meters of tunnelling was planned for each day?a)48 mb)40 mc)36 md)38 mCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A tunnel of length 360 m is to be constructed. As per the plan, the team has to completethe tunnellingwithin a specified period of time. For the first four days, the tunnelling was done according to the plan. However, it was found that the resources were being underutilized. It was then decided that the rate of tunnelling should be increased and then they started tunnelling 15 m more than their everyday plan. Therefore, a day before the planned date they had tunnelled to a length of 380 m. How many meters of tunnelling was planned for each day?a)48 mb)40 mc)36 md)38 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tunnel of length 360 m is to be constructed. As per the plan, the team has to completethe tunnellingwithin a specified period of time. For the first four days, the tunnelling was done according to the plan. However, it was found that the resources were being underutilized. It was then decided that the rate of tunnelling should be increased and then they started tunnelling 15 m more than their everyday plan. Therefore, a day before the planned date they had tunnelled to a length of 380 m. How many meters of tunnelling was planned for each day?a)48 mb)40 mc)36 md)38 mCorrect answer is option 'B'. Can you explain this answer?.
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