Page 21 - Start Up Mathematics_7

Solution: Temperature at noon = +10°C
Required temperature = –6°C

Total decrease in temperature = 10 – (–6) = 16°C
Let the decrease of 16°C takes place in n hours.
Rate of decrease of temperature = 2°C/h
∴ 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 27: 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 Do you know?

Number of correct answers = 8 The study room of the famous
3(C) – 2(I) = Marks scored mathematician Sir Isaac Newton in
⇒ 3(8) – 2(I) = 20 the Royal Society, which had not
been used since his death, was made
⇒ 24 – 20 = 2(I) available to Indian mathematician
⇒ 4 = 2(I) Srinivasa Ramanujan.
⇒ I = 2

∴ Upasana attempted 2 questions incorrectly.
Example 28: An elevator descends into a mine shaft at the rate of 8 m per min. If the descent
starts from 16 m above the ground level, how long will it take to reach –240 m?
Solution: Total distance to be covered = 16 – (–240) = 256 m
Elevator descends at the rate of 8 m per min
(240 + 16) m
∴ Required time to reach at –240 m = = 32 min
8 m/ min

EXERCISE 1.4

1. Divide the following:
(a) 75 by –5 (b) –36 by –12 (c) 34 by –17 (d) 0 by –98

2. Fill in the blanks:
(a) 45 ÷ ______ = –5 (b) ______ ÷ (–12) = 5 (c) 23 ÷ ______ = –1
(d) –11 ÷ ______ = 1 (e) ______ ÷ (–2) = 38
3. State true or false for each of the following:

(a) 0 ÷ 7 = 0 (b) (–18) ÷ 0 = 0 (c) 0 ÷ 0 = 0 (d) (–10) ÷ (–2) = 5

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