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Mathematics

Aditya went to Australia during the holidays of his children. They visited the coral reef and they were all excited to go for scuba diving. Aditya dived 36 feet to reach the brain coral as his instructor had directed him. He then rose by 19 feet to travel over a ridge.

(1) What is the depth of the ridge ?

  1. 57 feet
  2. 19 feet
  3. 17 feet
  4. 45 feet

(2) Aditya again dived 58 feet to reach the base of the reef. What is the depth of the reef ?

  1. 32 feet
  2. 41 feet
  3. 58 feet
  4. 75 feet

(3) In order to see an underwater cave, Aditya rose 26 feet. What is his location with respect to sea-level ?

  1. 49 feet
  2. 101 feet
  3. 26 feet
  4. 9 feet

(4) If a whale moving at a depth of 21 feet from the sea level passed over Aditya, what was its distance from Aditya ?

  1. 64 feet
  2. 49 feet
  3. 53 feet
  4. 28 feet

Integers

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Answer

(1) Given:

Initial depth = -36 feet \hspace{1cm}(36 feet below sea level)

He rises 19 feet = +19

Depth = -36 + 19 = -17 \hspace{1cm}(17 feet below sea level)

Depth = 17 feet

Hence, option 3 is the correct option.

(2) Starting position = -17 feet \hspace{1cm}(from the previous step)

Again he dives 58 feet = -58 feet \hspace{1cm}(Given)

Depth = -17 + (-58)
= -17 - 58
= -(17 + 58) = -75 feet

Depth = 75 feet

Hence, option 4 is the correct option.

(3) Starting position = -75 feet \hspace{1cm}(from the previous step)

He rises by 26 feet = +26 \hspace{1.5cm}(Given)

Location = -75 + 26 = -49

Location = 49 feet below the sea level

Hence, option 1 is the correct option.

(4) Given:

Whale's position: -21 feet
Aditya's position: -49 feet (from the previous step)

Distance of Whale from Aditya = -21 - (-49)

= -21 + 49 = 28

Distance of Whale from Aditya = 28 feet

Hence, option 4 is the correct option.

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