Page 23 - ICSE Math 7

Example 13: The temperature at noon was 10°C. If it decreases at the rate of 2°C per hour until
midnight, at what time would the temperature be 6°C below zero? What would be the
temperature at midnight?
Solution: Temperature at noon = +10°C
Required temperature = –6°C
Total decrease in temperature = 10°C – (–6°C) = 16°C
Let the decrease of 16°C takes place in n hours.
Rate of decrease of temperature = 2°C per hour
∴ 2n = 16 ⇒ n = 8
∴ The time at 8 hours passed noon = 8 p.m.
Total decrease until midnight = 12 × 2°C = 24°C
Temperature at midnight = 10°C – 24°C = –14°C

Example 14: In a class test 3 marks are awarded for every correct answer, 2 marks are deducted for
every incorrect answer and no marks are given for not attempting a question. Upasana
scored 20 marks. If she has got 8 correct answers, how many questions has she attempted
incorrectly?

Solution: Marks for one correct answer = +3
Marks for one incorrect answer = –2
If C = number of correct answers, I = number of incorrect answers, then
3(C) – 2(I) = Marks scored
Marks scored by Upasana = 20
Number of correct answers = 8
3(C) – 2(I) = Marks scored
⇒ 3(8) – 2(I) = 20
⇒ 24 – 20 = 2(I)
⇒ 4 = 2(I)
⇒ I = 2
∴ Upasana attempted 2 questions incorrectly.

EXERCISE 1.3

1. In a competitive examination, 5 marks are awarded for each correct answer, 2 marks are deducted
for each incorrect answer and no marks are given for a question which is not attempted. Answer
the following questions.
(a) Nishi appeared in the examination and attempted 12 questions correctly and 5 questions
incorrectly. However she did not attempt 3 questions. What will be her score?
(b) Rohan attempted 7 questions correctly and 9 questions incorrectly. He did not attempt
4 questions. What will be his score?
2. The temperature of a piece of metal is –13°C. On heating, the temperature of the metal rises to
63°C:
(a) What is the change in temperature of the metal piece?
(b) What temperature of the metal would be exactly between the initial and final temperatures?
(c) Calculate the temperature of the metal if it rises by 63°C.

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