Applications (Word Problem)

Q. Question 8
In countries like USA and Canada, the temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:
$F=\frac{9}{5}C+32$
(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis.
(ii) If the temperature is ${30}^{\circ }C$, what is the temperature in Fahrenheit?
(iii) If the temperature is ${95}^{\circ }F$, what is the temperature in Celsius?
(iv) If the temperature is $0^{\circ }C$, what is the temperature in Fahrenheit and if the temperature is $0^{\circ }F$, what is the temperature in Celsius?
(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

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Question 99

The length of a rectangle is two times its width. The perimeter of the rectangle is 180 cm. Find the dimensions of the rectangle.

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Question 95

A man travelled two-fifth of his journey by train, one-third by bus, one-fourth by car and the remaining 3 km on foot. What is the length of his total journey?

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The sum of three consecutive numbers is $36$. Find the numbers.

1. $12$

2. $11$

3. $13$

4. $10$

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A is elder to B by $2$ years. A’s father F is twice as old as A and B is twice as old as his sister S. If the age of the father and sister differs by $40$ years, find As age.

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Question 3(ii)
Solve the following :
Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age . What is Laxmi’s age?

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Question 93

Two-third of a number is greater than one-third of the number by 3. Find the number.

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Question 98

A girl is 28 years younger than her father. The sum of their ages is 50 years. Find the ages of the girl and her father.

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Question 73

In a school, the number of girls is 50 more than the number of boys. The total number of students is 1070. Find the number of girls.

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Question 77

After 25 years, Rama will be 5 times as old as he is now. Find his present age.

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Question 86

Solve the following:

The sum three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.

Q. If $\frac{2}{3}$ of a number is 10, then what is 1.75 times of that number?

Q. Question 3(i)
Solve the following:
Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?

Q. What should be added to (-7/8) so as to get (5/9)?

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Question 79

My younger sister's age today is 3 times what it will be 3 years from now minus 3 times what her age was 3 years ago. Find her present age.

Q.

Find the measure of an angle which is equal to its complement?

Q. Rohan's mother is $12$ years more than twice his age. After $8$ years, his mother’s age will be $20$ years less than thrice his age. Find Rohan's age and his mother’s age.

1. $\text{16 and 48}$
2. $\text{16 and 44}$
3. $\text{12 and 36}$
4. $\text{54 and 14}$

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Question 70

Seven times a number is 12 less than thirteen times the same number. Find the number.

Q. Question 2(b)
Solve the following :
In an isosceles triangle, the base angles are equal. The vertex angle is ${40}^{\circ }$. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is ${180}^{\circ }$.

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Question 90

Two complementary angles differ by ${20}^{\circ }.$ Find the angles.

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Question 86

A number, when divided by 6, gives the quotient 6. What is the number?

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Question 85

The sum of three consecutive integers is 5 more than the smallest of the integers. Find the integers.

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Question 92

In a class of 60 students, the number of girls is one third the number of boys. Find the number of girls and boys in the class.

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Question 69

A number exceeds the other number by 12. If their sum is 72, find the numbers.

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Question 94

A number is as much greater than 27 as it is less than 73. Find the number.

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Question 82

In a bag, the number of one rupee coins is three times the number of two rupees coins. If the worth of the coins is Rs. 120, find the number of 1 rupee coins.

Q. Question 2(c)
Solve the following
Smita’s mother is 34 years old. Two years from now mother’s age will be 4 times Smita’s present age. What is Smita’s present age?

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Question 97

Thrice a number decreased by 5 exceeds twice the number by 1. Find the number.

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Question 2(d)
Solve the following :
Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

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Question 80

If 45 is added to half a number, the result is triple the number. Find the number.