Maths
maths maharashtra board 10th
- A boat requires 6 hrs to travel 36 km downstream and 24 km upstream. It requires 9 hrs to travel 48 km down Answer: Speed of boat in still water = 10 km/hr, speed of stream = 2 km/hr Let the speed of the boat in still water be x km/hr and of the st... 1
- A two – digit number is 4 times the sum of its digits. The number obtained by interchanging the digits is greater Answer: The original number is 12. Let the tens digit be x and the units digit y . The number is 10x + y . Number is 4 times the sum of digi... 1
- The perimeter of a rectangle is 40 cm and its length is 5 cm more than twice its breadth. Find the length and the Let's solve the problem step by step: Let the breadth of the rectangle be 'x' cm, and the length be 'y' cm. Given information: The perimeter... 1
- A certain amount is distributed equally among certain boys. If there were 5 boys more each would have received Rs. 8 Answer: 20 boys and Rs. 800 distributed Let there be x boys, each getting Rs. y . Amount = xy . 5 more boys, Rs. 8 less each: (x + 5)(y - 8)... 1
- If 1 is added to the numerator of a certain fraction, it becomes ½. Instead, if 5 are Answer: The fraction is 3/8. Let the fraction be x/y . x + 1/y = 1/2 ⇒ y = 2x + 2 (1) x/y - 5 = 1 ⇒ x = y - 5 (2) Substitute (1) in (2): x =... 1
- Students were standing in rows for P.T exercises. If 4 students were less in each row, 10 more rows were required and Answer: 800 students Let there be x students in each row and y rows. Total students = xy . 4 fewer per row needs 10 more rows: (x - 4)(y + 1... 1
- Some amount is distributed equally among some boys. If 10 boys were more each would get Rs. 2 less and each Answer: 40 boys and Rs. 400 distributed Let there be x boys, each getting Rs. y . Amount = xy . 10 more boys, Rs. 2 less each: (x + 10)(y -... 1
- The value of the fraction becomes 2/5, if 2 is subtracted from its numerator and the value becomes ½, if 1 is Answer: The fraction is 8/15. Let the fraction be x/y . x - 2/y = 2/5 ⇒ 5x - 10 = 2y (1) x/y + 1 = 1/2 ⇒ y = 2x - 1 (2) Substitute (2) in (1... 1
- If one is subtracted from the numerator and denominator, the value of the fraction becomes 1/3. Answer: The fraction is 5/13. Let the fraction be x/y . x - 1/y - 1 = 1/3 ⇒ 3x - 3 = y - 1 ⇒ y = 3x - 2 (1) x + 3/y + 3 = 1/2 ⇒ 2x + 6 = y +... 1
- If the numerator of a fraction is decreased by 1, its value becomes ½ and if its denominator is increased by 7, its Answer: The fraction is 5/8. Let the fraction be x/y . x - 1/y = 1/2 ⇒ y = 2x - 2 (1) x/y + 7 = 1/3 ⇒ 3x = y + 7 (2) Substitute (1) in (2):... 1
- 3 pens and 4 pencils cost Rs. 38, while 2 pens and 5 pencils cost Rs. 30. Answer: Pen = Rs. 10, Pencil = Rs. 2 Let a pen cost Rs. x and a pencil Rs. y . 3x + 4y = 38 (1) 2x + 5y = 30 (2) Multiply (1) by 2 and (2) b... 1
- Ramesh distributed certain number of pencil among his friends. If the number of friends were 4 more, then each would Answer: 12 friends and 48 pencils Let the number of friends be x and the pencils each gets be y . Total pencils = xy . 4 more friends, 1 pen... 1
- If I divide the sum of two numbers by 3, the quotient is 4 and the remainder 1. Let's solve the problem step by step: Let the two numbers be represented by 'x' and 'y'. Given information: When the sum of two numbers is d... 1
- The length of a rectangle is less than twice its breadth by 9cm. The perimeter of the rectangle is 54 cm Answer: Area = 180 cm² Let the breadth be x cm. The length is 9 cm less than twice the breadth: length = 2x - 9 cm. 2(2x - 9 + x) = 54 3x -... 1
- 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 Let John's age be represented as 'x' years, and his father's age be represented as 'y' years. Given conditions: John's father is three times... 1
- On the first day of the sale of tickets of a drama, 50 tickets in all were sold. Answer: 10 tickets at Rs. 20 and 40 tickets at Rs. 40 Let x tickets be sold at Rs. 20 and y tickets at Rs. 40. x + y = 50 (1) 20x + 40y = 18... 1
- Sum of two numbers is 200. 1/3 of greater number is equal to ½ of smaller number. Find the numbers. Ans. 120 & 80. Answer: The numbers are 120 and 80. Let the greater number be x and the smaller y . x + y = 200 (1) x/3 = y/2 ⇒ 2x = 3y (2) From (2), x = 3y... 1
- If 3 is added to the numerator and 5 is subtracted from the denominator of a fraction, the value of the fraction become Answer: The original fraction is 6/17. Let the fraction be x/y . First condition: x + 3/y - 5 = 3/4 ⇒ 4x + 12 = 3y - 15 , i.e. 4x - 3y = -27... 1
- Some postcards costing 25 paise each and inland letters costing Rs. 2 each were purchased for Rs. 53 Answer: The amount would be Rs. 7 less (Rs. 46 instead of Rs. 53). Let x = number of postcards (Rs. 0.25 each) and y = number of inland lett... 1
- The sum of the present ages of Mangesh and his mother is 70 years. Seven years ago mother’s age was three Let Mangesh age be 'x' years and his Mother's age be 'y' years Given Condition's sum of mangesh age and his mother age is 70 years x+y=70 --... 1
- Mother’s age is 4 times her daughter’s age. 16 years hence mother’s age will be twice her daughter’s age at Answer: Mother is 32 years old and daughter is 8 years old. Let the daughter's present age be x years and the mother's y years. y = 4x (1) A... 1
- 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. Answer: 7 litres at Rs. 15 per litre and 3 litres at Rs. 12 per litre Let x litres be sold at Rs. 15 and y litres at Rs. 12. x + y = 10 (1)... 1
- 3 pepsi and 1 mangola bottles together cost Rs. 53, but 2 pepsi and 4 mangola bottles cost Rs. 62. Answer: Pepsi bottle = Rs. 15, Mangola bottle = Rs. 8 Let a Pepsi bottle cost Rs. x and a Mangola bottle Rs. y . 3x + y = 53 (1) 2x + 4y = 6... 1
- 3 books and 1 notebook together cost Rs. 53, but 2 books and 4 notebooks cost Rs. 62. Find the cost of a book Answer: Book = Rs. 15, Notebook = Rs. 8 Let a book cost Rs. x and a notebook Rs. y . 3x + y = 53 (1) 2x + 4y = 62 (2) From (1), y = 53 - 3x... 1