Exercise 1.7
1. In a class test containing 15 questions, 4 marks are given for every correct answer and (-2) marks are given for every incorrect answer.
(i)
(i) Bharathi attempts all questions but only 9 answers are correct. What is her total score?
Solution :
Given:
Total questions:
Marks for a correct answer: +
Marks for an incorrect answer:
Correct answers by Bharathi:
Incorrect answers: 15 − 9 =
Calculate Marks for Correct Answers
9 × 4 =
Calculate Marks for Incorrect Answers
6 × (-2) =
Calculate Total Score
36 + (-12) = 36 −12 =
Bharathi's total score is 24 marks.
(ii)
(ii) One of her friends Hema attempts only 5 questions and all are correct. What will be her total score?
Solution:
Given:
Marks for a correct answer: +
Marks for an incorrect answer:
Total questions attempted by Hema:
Correct answers:
Incorrect answers:
Calculate Marks for Correct Answers
5 × 4 =
Calculate Marks for Incorrect Answers
Since there are no incorrect answers, the marks deducted are:
0 × (−2) =
Calculate Total Score: 20 + 0 =
Hema's total score is 20 marks.
2. A cement company earns a profit of ₹ 9 per bag of white cement sold and a loss of ₹ 5 per bag of grey cement sold
(i)
(i) The company sells 7000 bags of white cement and 6000 bags of grey cement in a month. what is its profit or loss?
Solution:
Given:
Profit per bag of white cement = ₹
Loss per bag of grey cement = ₹
Bags of white cement sold =
Bags of grey cement sold =
Calculate total profit from white cement
Total Profit = 7,000 × 9 =
Calculate total loss from grey cement
Total Loss = 6,000 × 5 =
Find net profit or loss
= 63,000 − 30,000
=
Since the result is positive, the company makes a profit of ₹33,000 in a month.
(ii)
(ii) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 5400
Solution:
Given Data:
Profit per bag of white cement = ₹
Loss per bag of grey cement = ₹
Bags of grey cement sold =
Calculate the Total Loss from Grey Cement
Total Loss = 5,400 × 5 =
Find the Required Number of White Cement Bags
Let x be the number of white cement bags needed to make the total profit equal to ₹27,000.
Total Profit = x × 9
Since there is no profit or loss, the total profit must equal the total loss:
x × 9 = 27,000
Solve for x
x =
The company must sell 3,000 bags of white cement to have neither profit nor loss.
3. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at which time would the temperature be 8°C below zero? What would be the temperature at midnight?
Solution:
Given Data:
Temperature at 12 noon: +
Rate of decrease:
Target temperature:
Find the Time When the Temperature Reaches -8°C
Let x be the number of hours after 12 noon when the temperature reaches -8°C.
Using the equation:
Final Temperature=Initial Temperature−(Rate of decrease×Hours) −8=10−(2×x)
Solving for x:
−8 − 10 = −2x
x =
So, the temperature reaches -8°C after 9 hours, which means: 12 noon +9 hours =
Find the Temperature at Midnight (12 AM)
Midnight is 12 hours after 12 noon. Using the same formula:
Temperature at midnight =10 − (2×12) = 10 −24 =
The temperature reaches -8°C at 9 PM.
The temperature at midnight (12 AM) is -14°C.
4. In a class test (+3) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question.
(i)
(i) Radhika scored 20 Marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?
Solution:
Given Data:
Marks for a correct answer = +3
Marks for an incorrect answer = -2
Total marks scored by Radhika =
Number of correct answers =
Let the number of incorrect answers be = x
Calculate Marks from Correct Answers
Marks from correct answers = 12 × 3 =
Use the Total Score Equation
Total Marks=(Marks from correct answers)+(Marks from incorrect answers) 20 = 36 + (x × − 2)
Solve for x
20 − 36 = −2x
x =
Radhika attempted 8 questions incorrectly.
(ii)
(ii) Mohini scores (-5) marks in this test, though she has got 7 correct answers.How many questions has she attempted incorrectly?
Solution:
Given Data:
Marks for a correct answer = +
Marks for an incorrect answer =
Total marks scored by Mohini =
Number of correct answers =
Let the number of incorrect answers be = x
Calculate Marks from Correct Answers
Marks from correct answers = 7 × 3 =
Use the Total Score Equation
Total Marks = (Marks from correct answers)+(Marks from incorrect answers) −5 = 21+(x × −2)
Solve for x
−5 − 21 = −2x
x =
Mohini attempted 13 questions incorrectly.
5. An elevator descends into a mine shaft at the rate of 6 meters per minute. If the descent starts from 10 m above the ground level, how long will it take to reach - 350 m
Solution:
Given Data:
Starting position = 10 m above ground (+10 m)
Final position =
Rate of descent =
Find the Total Distance to Descend
The elevator moves from +10 m to -350 m, so the total distance covered is:
Total Distance=10−(−350) = 10 + 350 =
Calculate Time Required
Time =
=
The elevator will take 60 minutes (or 1 hour) to reach -350 m.