text: ### Linear equation word problems for practice
  
  1.  Suresh scored 15 marks more than Ramesh in Mathematics. If the sum of their marks in Mathematics is 275, find the marks obtained by each of them. Ans. Suresh :- 145; Ramesh :- 130 marks
  2.  The sum of two numbers is 40 and the greater number is thrice the smaller number. Find the numbers. Ans. The greater number is 30 & the smaller number is 10.
  3.  The sum of the two numbers is 25 and the difference between them is 15. Find the two numbers. Ans. The greater number is 20 and the smaller number is 5.
  4.  The length of a rectangle is greater than twice its breadth by 4 cm. If the perimeter of the rectangle is 26 cm, find its length and breadth. Ans. Length of the rectangle is 10cm & its breadth is 3 cm.
  5.  The sum of the present ages of Ram and Shyam is 36 years. Ram is elder than Shyam by 2 years. Find their present ages. Ans. The present age of Ram is 19 yrs. And Shyam is 17 years.
  6.  Ram has in all 35 coins, some of denomination 25 paise and some of 10 paise. Total amount is Rs. 6.20. Find the number of coins of each kind. Ans. 25 paise coins; - 18 and 10 paise coins: - 17.
  7.  Cost of a table is three times the cost of a chair. One table and one chair together cost Rs. 800. Find the cost of a table.  Ans. 600
  8.  The perimeter of an isosceles triangle is 43cm. The length of its each congruent side is 1 cm less than twice the length of its base. Find the length of each side of the triangle. Ans. 17 cm, 9 cm, 17 cm.
  9.  The difference between two numbers is 5. Six times the smaller number is equal to four times the greater. Find the numbers. Ans. 15 and 10.
  10.              In a right – angled triangle, one of the acute angles exceeds the other by 200. Find the measure of the acute angles. Ans. 350 & 550.
  
  1.  The perimeter of an isosceles triangle is 27 cm and the length of the congruent sides is greater than twice the length of the base by 1 cm. Find the length of each side of the triangle. Ans. 11 cm, 11cm and 5 cm.
  2.  Ina a cyclic quadrilateral ABCD, measure of angle A is double the measure of angle C. Find the measure of angle A and angle C. Ans. 1200 & 600.
  3.  The sum of two numbers is 70. Three times the greater number is equal to four times the smaller number. Find the two numbers. Ans. 40 and 30.
  4.  The difference between two numbers is 16. The greater number is 1 more than twice the smaller number. Find the numbers. Ans. 31 and 15.
  5.  2 pens and 3 pencils cost Rs. 26, while 3 pens and 2 pencils cost Rs. 34. Find the cost of a pen and a pencil. Ans. Pen: - Rs. 10 Pencil: - Rs. 2.
  6.  In a parallelogram ABCD, the measure of angle A is thrice the measure of angle B. Find the measure of angle A and angle B. Ans. Angle A :- 1350 & angle B :- 450.
  7.  A piece of string 12m in length was cut into two pieces such that one piece is x metres and the other is y meters. If y is 2 meters more than x, find the length of each piece. Ans. 5m and 7 m.
  8.  The difference between the measures of angle A and angle B of a parallelogram ABCD is 180. Find the measure of angle A and angle B. Ans. Angle A: - 990 and Angle B: - 810.
  9.  2 mangles and 5 oranges together cost Rs. 30; but 4 mangoes and 3 oranges cost Rs. 46. Find the cost of a mango and an orange. Ans. Mango 10Rs, Orange 2 Rs.
  10.              3 books and 1 notebook together cost Rs. 53, but 2 books and 4 notebooks cost Rs. 62. Find the cost of a book and a note book. Ans. Book Rs. 15, Note book Rs. 8.
  
  1.  3 pepsi and 1 mangola bottles together cost Rs. 53, but 2 pepsi and 4 mangola bottles cost Rs. 62. Find the cost of a pepsi and a mangola bottle. Ans. Cost of pepsi bottle: - Rs. 15 Mangola bottle: - Rs. 8.
  2.  Out of 10 litres, a milkman sells some milk at the rate of Rs. 15 per litre and some at the rate of Rs.12 per litre. He gets Rs. 141 on selling it. Find the quantity of milk he sold at each rate. Ans. 7 litres @ Rs. 15 per litre and 3 litres @ Rs. 12 per litres.
  3.  Mother’s age is 4 times her daughter’s age. 16 years hence mother’s age will be twice her daughter’s age at that time. Find their present ages. Ans. Mother’s present age ; 32 years. daughter’s present age : 8 years.
  4.  The sum of the present ages of Mangesh and his mother is 70 years. Seven years ago mother’s age was three times the age of Mangesh at that time. Find their present ages. Ans. Mangesh: - 21 years. Mother: - 49 years.
  5.  Some postcards costing 25 paise each and inland letters costing Rs. 2 each were purchased for Rs. 53. Total number of postcards and inland letters purchased was 44. If the number of postcards and inland letters is interchanged, how much less would be the amount? Rs. 7 less.
  6.  If 3 is added to the numerator and 5 is subtracted from the denominator of a fraction, the value of the fraction becomes ¾ and if 1 is added to the numerator and 3 is subtracted from the denominator, the value of the fraction becomes ½. Find the original fraction. Ans. The original fraction is 6/17.
  7.  Sum of two numbers is 200. 1/3 of greater number is equal to ½ of smaller number. Find the numbers. Ans. 120 & 80.
  8.  On the first day of the sale of tickets of a drama, 50 tickets in all were sold. If the rates of the tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs. 1,800, find the number of tickets sold at each rate.  Ans. 10 tickets @ Rs. 20,       40 tickets @ Rs. 40.
  9.  Age of John’s father is three times the age of John. Five years ago, age of father was four times John’s age at that time. Find their present ages. Ans. Father’s age :- 45 yrs.  John’s age :- 15 yrs. B
  10.               The length of a rectangle is less than twice its breadth by 9cm. The perimeter of the rectangle is 54 cm. Find the area of the rectangle. Ans. Area is 180 sq cm.
  
  1.  If I divide the sum of two numbers by 3, the quotient is 4 and the remainder 1. If I divide the difference of these two numbers by 2, the quotient is 2 and the remainder 1. Find the number. Ans. 9 and 4.
  2.  Ramesh distributed certain number of pencil among his friends. If the number of friends were 4 more, then each would have got 1 pencil less. But if the number of friends were 4 less, then each would have received 2 pencils more. Find the number of friends and total number of pencils distributed.  Ans. Friends :- 12 pencils : 48
  3.  3 pens and 4 pencils cost Rs. 38, while 2 pens and 5 pencils cost Rs. 30. Find the cost of each pen and each pencil. Ans. Pen Rs. 10 and Pencil Rs. 2.
  4.  If the numerator of a fraction is decreased by 1, its value becomes ½ and if its denominator is increased by 7, its value becomes 1/3. Find that fraction. Ans. The fraction is 5/8.
  5.  If one is subtracted from the numerator and denominator, the value of the fraction becomes 1/3. When 3 is added to its numerator and denominator, the value becomes ½. Find the fraction. Ans. The fraction is 5/13.
  6.   The value of the fraction becomes 2/5, if 2 is subtracted from its numerator and the value becomes ½, if 1 is added to its denominator. Find the fraction. Ans. 8/15.
  7.  Some amount is distributed equally among some boys. If 10 boys were more each would get Rs. 2 less and each would get Rs. 6 more if 15 boys were less. Find the amount distributed and the number of boys. Ans. 40 boys and Rs. 400.
  8.  Students were standing in rows for P.T exercises. If 4 students were less in each row, 10 more rows were required and if 5 students were more in each row, then the number of rows were reduced by 8. Find the number of students. Ans. 800 students.
  9.  If 1 is added to the numerator of a certain fraction, it becomes ½. Instead, if 5 are subtracted from its denominator, it becomes 1. Find the fractions. Ans. 3/8
  10.              A certain amount is distributed equally among certain boys. If there were 5 boys more each would have received Rs. 8 less, while if there were 4 boys less, each would have received Rs. 10 more. Find the amount distributed and the number of boys. Ans. Rs. 800 boys 20.
  11.              The perimeter of a rectangle is 40 cm and its length is 5 cm more than twice its breadth. Find the length and the breadth of the rectangle. Ans. Length = 15cm and breadth = 5 cm.
  12.              A two – digit number is 4 times the sum of its digits. The number obtained by interchanging the digits is greater by 9 than the original number. Find the original number. Ans. The original number is 12.
  13.              A boat requires 6 hrs to travel 36 km downstream and 24 km upstream. It requires 9 hrs to travel 48 km downstream and 40 km upstream. Find the speed of the stream and that of the boat in the still water. Ans. Speed of the Boat = 10Km/ hr. and the speed of the stream = 2 Km/ hr.
explanation: The document is a collection of linear equation word problems, each followed by its answer. Each problem presents a real-world scenario that can be solved using linear equations, and the answers are provided for verification.
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distilabel_metadata.content: ### Linear equation word problems for practice
  
  1.  Suresh scored 15 marks more than Ramesh in Mathematics. If the sum of their marks in Mathematics is 275, find the marks obtained by each of them. Ans. Suresh :- 145; Ramesh :- 130 marks
  2.  The sum of two numbers is 40 and the greater number is thrice the smaller number. Find the numbers. Ans. The greater number is 30 & the smaller number is 10.
  3.  The sum of the two numbers is 25 and the difference between them is 15. Find the two numbers. Ans. The greater number is 20 and the smaller number is 5.
  4.  The length of a rectangle is greater than twice its breadth by 4 cm. If the perimeter of the rectangle is 26 cm, find its length and breadth. Ans. Length of the rectangle is 10cm & its breadth is 3 cm.
  5.  The sum of the present ages of Ram and Shyam is 36 years. Ram is elder than Shyam by 2 years. Find their present ages. Ans. The present age of Ram is 19 yrs. And Shyam is 17 years.
  6.  Ram has in all 35 coins, some of denomination 25 paise and some of 10 paise. Total amount is Rs. 6.20. Find the number of coins of each kind. Ans. 25 paise coins; - 18 and 10 paise coins: - 17.
  7.  Cost of a table is three times the cost of a chair. One table and one chair together cost Rs. 800. Find the cost of a table.  Ans. 600
  8.  The perimeter of an isosceles triangle is 43cm. The length of its each congruent side is 1 cm less than twice the length of its base. Find the length of each side of the triangle. Ans. 17 cm, 9 cm, 17 cm.
  9.  The difference between two numbers is 5. Six times the smaller number is equal to four times the greater. Find the numbers. Ans. 15 and 10.
  10.              In a right – angled triangle, one of the acute angles exceeds the other by 200. Find the measure of the acute angles. Ans. 350 & 550.
  
  1.  The perimeter of an isosceles triangle is 27 cm and the length of the congruent sides is greater than twice the length of the base by 1 cm. Find the length of each side of the triangle. Ans. 11 cm, 11cm and 5 cm.
  2.  Ina a cyclic quadrilateral ABCD, measure of angle A is double the measure of angle C. Find the measure of angle A and angle C. Ans. 1200 & 600.
  3.  The sum of two numbers is 70. Three times the greater number is equal to four times the smaller number. Find the two numbers. Ans. 40 and 30.
  4.  The difference between two numbers is 16. The greater number is 1 more than twice the smaller number. Find the numbers. Ans. 31 and 15.
  5.  2 pens and 3 pencils cost Rs. 26, while 3 pens and 2 pencils cost Rs. 34. Find the cost of a pen and a pencil. Ans. Pen: - Rs. 10 Pencil: - Rs. 2.
  6.  In a parallelogram ABCD, the measure of angle A is thrice the measure of angle B. Find the measure of angle A and angle B. Ans. Angle A :- 1350 & angle B :- 450.
  7.  A piece of string 12m in length was cut into two pieces such that one piece is x metres and the other is y meters. If y is 2 meters more than x, find the length of each piece. Ans. 5m and 7 m.
  8.  The difference between the measures of angle A and angle B of a parallelogram ABCD is 180. Find the measure of angle A and angle B. Ans. Angle A: - 990 and Angle B: - 810.
  9.  2 mangles and 5 oranges together cost Rs. 30; but 4 mangoes and 3 oranges cost Rs. 46. Find the cost of a mango and an orange. Ans. Mango 10Rs, Orange 2 Rs.
  10.              3 books and 1 notebook together cost Rs. 53, but 2 books and 4 notebooks cost Rs. 62. Find the cost of a book and a note book. Ans. Book Rs. 15, Note book Rs. 8.
  
  1.  3 pepsi and 1 mangola bottles together cost Rs. 53, but 2 pepsi and 4 mangola bottles cost Rs. 62. Find the cost of a pepsi and a mangola bottle. Ans. Cost of pepsi bottle: - Rs. 15 Mangola bottle: - Rs. 8.
  2.  Out of 10 litres, a milkman sells some milk at the rate of Rs. 15 per litre and some at the rate of Rs.12 per litre. He gets Rs. 141 on selling it. Find the quantity of milk he sold at each rate. Ans. 7 litres @ Rs. 15 per litre and 3 litres @ Rs. 12 per litres.
  3.  Mother’s age is 4 times her daughter’s age. 16 years hence mother’s age will be twice her daughter’s age at that time. Find their present ages. Ans. Mother’s present age ; 32 years. daughter’s present age : 8 years.
  4.  The sum of the present ages of Mangesh and his mother is 70 years. Seven years ago mother’s age was three times the age of Mangesh at that time. Find their present ages. Ans. Mangesh: - 21 years. Mother: - 49 years.
  5.  Some postcards costing 25 paise each and inland letters costing Rs. 2 each were purchased for Rs. 53. Total number of postcards and inland letters purchased was 44. If the number of postcards and inland letters is interchanged, how much less would be the amount? Rs. 7 less.
  6.  If 3 is added to the numerator and 5 is subtracted from the denominator of a fraction, the value of the fraction becomes ¾ and if 1 is added to the numerator and 3 is subtracted from the denominator, the value of the fraction becomes ½. Find the original fraction. Ans. The original fraction is 6/17.
  7.  Sum of two numbers is 200. 1/3 of greater number is equal to ½ of smaller number. Find the numbers. Ans. 120 & 80.
  8.  On the first day of the sale of tickets of a drama, 50 tickets in all were sold. If the rates of the tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs. 1,800, find the number of tickets sold at each rate.  Ans. 10 tickets @ Rs. 20,       40 tickets @ Rs. 40.
  9.  Age of John’s father is three times the age of John. Five years ago, age of father was four times John’s age at that time. Find their present ages. Ans. Father’s age :- 45 yrs.  John’s age :- 15 yrs. B
  10.               The length of a rectangle is less than twice its breadth by 9cm. The perimeter of the rectangle is 54 cm. Find the area of the rectangle. Ans. Area is 180 sq cm.
  
  1.  If I divide the sum of two numbers by 3, the quotient is 4 and the remainder 1. If I divide the difference of these two numbers by 2, the quotient is 2 and the remainder 1. Find the number. Ans. 9 and 4.
  2.  Ramesh distributed certain number of pencil among his friends. If the number of friends were 4 more, then each would have got 1 pencil less. But if the number of friends were 4 less, then each would have received 2 pencils more. Find the number of friends and total number of pencils distributed.  Ans. Friends :- 12 pencils : 48
  3.  3 pens and 4 pencils cost Rs. 38, while 2 pens and 5 pencils cost Rs. 30. Find the cost of each pen and each pencil. Ans. Pen Rs. 10 and Pencil Rs. 2.
  4.  If the numerator of a fraction is decreased by 1, its value becomes ½ and if its denominator is increased by 7, its value becomes 1/3. Find that fraction. Ans. The fraction is 5/8.
  5.  If one is subtracted from the numerator and denominator, the value of the fraction becomes 1/3. When 3 is added to its numerator and denominator, the value becomes ½. Find the fraction. Ans. The fraction is 5/13.
  6.   The value of the fraction becomes 2/5, if 2 is subtracted from its numerator and the value becomes ½, if 1 is added to its denominator. Find the fraction. Ans. 8/15.
  7.  Some amount is distributed equally among some boys. If 10 boys were more each would get Rs. 2 less and each would get Rs. 6 more if 15 boys were less. Find the amount distributed and the number of boys. Ans. 40 boys and Rs. 400.
  8.  Students were standing in rows for P.T exercises. If 4 students were less in each row, 10 more rows were required and if 5 students were more in each row, then the number of rows were reduced by 8. Find the number of students. Ans. 800 students.
  9.  If 1 is added to the numerator of a certain fraction, it becomes ½. Instead, if 5 are subtracted from its denominator, it becomes 1. Find the fractions. Ans. 3/8
  10.              A certain amount is distributed equally among certain boys. If there were 5 boys more each would have received Rs. 8 less, while if there were 4 boys less, each would have received Rs. 10 more. Find the amount distributed and the number of boys. Ans. Rs. 800 boys 20.
  11.              The perimeter of a rectangle is 40 cm and its length is 5 cm more than twice its breadth. Find the length and the breadth of the rectangle. Ans. Length = 15cm and breadth = 5 cm.
  12.              A two – digit number is 4 times the sum of its digits. The number obtained by interchanging the digits is greater by 9 than the original number. Find the original number. Ans. The original number is 12.
  13.              A boat requires 6 hrs to travel 36 km downstream and 24 km upstream. It requires 9 hrs to travel 48 km downstream and 40 km upstream. Find the speed of the stream and that of the boat in the still water. Ans. Speed of the Boat = 10Km/ hr. and the speed of the stream = 2 Km/ hr.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a collection of linear equation word problems, each followed by its answer. Each problem presents a real-world scenario that can be solved using linear equations, and the answers are provided for verification.
  
  Label: multiple-question-and-answer