Linear Equation...

Solve for x:

A number is 147 more than the average of its quarter, one-fifth and one-tenth. Find the number.

If of a number is 15 less than the original number, then the number is

Solve for x: 5(2x + 1) + 5(4x - 3) = 7(5x + 2) - 9(5x + 1) + 10x

The number 391 is divided into two parts in the ratio 5 : 12. The product of the two numbers is

If times a number is 30 more than the original number, then the number is

The perimeter of a rectangle is numerically equal to three-fourth of the area of the rectangle. If the length of the rectangle is cm, then its width is

A number whose sixth part exceeds its seventh part by 2 is

A number consists of two digits, whose sum is 15. If 27 is added to the original number, its digits get interchanged. Find the original number.

The denominator of a rational number is smaller than its numerator by 5. If 5 is added to the numerator and 3 is added to its denominator, the number becomes 2. What is the original rational number?

If, then X is equal to

A two-digit number is more than 20 but less than 30. Twice the sum of its digits is thrice their product. What is the number?

Find the two parts of 50 such that ^th of one part is equal to ^rd of the other.

If the angles of a triangle are in the ratio 5 : 5 : 8, then the sum of two smaller angles is

One-ninth of a number when subtracted from the number itself gives 48. Find the number.

Two teams appeared for the final round in a basketball tournament. One team got 71% points and was selected winner by a margin of 63 points. The total points were

Sam has £56. He shares it with his two friends, Jeff and Raghav, such that of the amount received by Jeff is equal to of the amount received by Raghav. Find out the respective amounts received by Jeff and Raghav.

Prateek is 48 years old. Shubham, his son, asks his father about his age, to which the father replies that after four years, he will be six years older than twice his age at that time. Find the present age of Shubham.

While navigating a boat in a river, Akhil travels 60 km downstream. The speed of the boat in still water is 30 km/hr. He then comes back to the same place from where he started. Find the speed of the stream if it takes four and a half hours to complete the journey.

There are a total of 84 apples and oranges in a basket, of which of the apples and of the oranges are used for making jam. The total number of apples and oranges of the same basket which are used for making jam is 60. How many apples are there in the basket?

Which of the following statements is/are CORRECT?

Statement (1): a = -1 is the solution of .

Statement (2): a = -5 is the solution of .

Fill in the blanks with the help of the table given below.

(1) The solution of the equation is ________.
(2) The value of the variable which satisfies a given equation is called ________ of the equation.
(3) Any term of an equation may be taken to the other side with its sign changed. This process is called _________.

	(1)	(2)	(3)
P		solution	equation
Q		solution	transposition
R		equation	transposition
S		transposition	solution

Directions: Read the following statements and find which of them are true or false with the help of the table given below.

(P) Multiplying both sides of an equation by a non-zero constant will change its solution.
(Q) The perimeter of a rectangle is 180 cm. If the length of the rectangle is decreased by 4 cm and its breadth is increased by 4 cm, the area of the rectangle decreases by 88 sq. cm. The length and the breadth of the rectangle are 36 cm and 54 cm, respectively.
(R) The sum of two numbers is 1880. If 7.5% of one number is 12.5% of the other number, then one of the numbers will be 1175.

Which of the following statements is INCORRECT?

(A) Raghu buys some t-shirts at the rate of Rs. 80 per t-shirt. He also buys an equal number of shirts at the rate of Rs. 100 per shirt. Then, he sells those t-shirts and shirts and makes a profit of 10% on t-shirts and 12% on shirts. At the end of the day, all t-shirts and shirts are sold out and his profit is Rs. 1240. Therefore, Raghu buys 62 t-shirts.
(B) A painter charges Rs. 7000 to paint the entire floor of the house. He works along with one labourer. The cost of materials used is Rs. 1800 and labour charges are Rs. 80 per hour. So, the painter will work for 65 hours.
(C) Rs. 280 is divided between x and y such that twice the y's share is less than x's share by Rs. 40. So, the y's share is Rs. 100.
(D) Aman thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. The number she thought of is 4.

Match the following:

Column - I	Column - II
(P) If , then a =	(i)
(Q) If , then z =	(ii)
(R) If , then m =	(iii)
(S) If , then x =	(iv)