Question: Some students planned a picnic. The budget for the food was Rs 2,500. As five of them unable to join the picnic, the cost of the food for each students increased by Rs 25. Find how many students went for the picnic? Solution: Let x number of students went for the picnic and the cost of the food for each student be Rs y. Ac…

Question: A piece of cloth costs Rs 800. If the piece was 5 m longer and the rate of cost of cloth per meter was Rs 8 less, the cost of the piece would have remained unchanged. How long is the piece and what is the rate of cost per meter? Solution: Given, A piece of cloth costs Rs 800. Let the length of the cloth be x m and the rate…

Question: The area of a rectangular field is 720 sq.m. and perimeter is 108 m. By what percent is the longer side of the field to be decreased to make it a square? Why? Solution: Given, Area of a rectangular field (A) = 720 m² Perimeter of the rectangular field (P) = 108 m Let 'l' represent the length of the field and 'b…

Question: The area of a right-angled triangle is 24 sq.cm. If the perpendicular of the triangle is 2cm shorter than its base, find two sides of a triangle. Solution: Given, Area of a right-angled triangle (A) = 24 cm² Let the length of the base (b) of the triangle be x cm. According to the question, the length of the perpendicular (…

Question: If the sides of a right-angled triangle are (x-2) cm, x cm, (x+2) cm, find the length of each of its side. Solution: Given, Sides of a right-angled triangle are (x-2) cm, x cm, and (x+2) cm. In a right-angled triangle, the longest side is represented as hypotenuse (h). Let, (x+2) be h, x be base (b) and (x-2) be perpendicu…

Question: A rectangular meadow has an area of 247 sq.m. and its perimeter is 64m, find the length and breadth of the meadow. Solution: Given, Area of the rectangular meadow (A) = 247 m² Perimeter of the meadow (P) = 64 m Let the length and breadth of the same rectangular meadow be l m and b m respectively. We have, P = 64 $or, 2(l+b…

Question: A rectangular piece of land is 40m long and 25m wide. A path of uniform width and 426 m² area surround the land from outside. Find the width of the path. Solution: Let x m represent the uniform width of the path. Given, Length of the rectangular land (l) = 40m Breadth of the rectangular land (b) = 25m We know, The uniform …

Question: The length of a room is 2m longer than its breadth. If the area of the room is 63sq.m. find the length and breadth of the room. Solution: Let the length of the room be l m and the breadth of that room be b m. According to the question, Condition I, Length is 2m longer than the breadth. $or, l = b+2$ - (i) Condition II, Are…

Question: The present ages of two brothers are 15 years and 22 years respectively. After how many years will the product of their ages be 408? Solution: Given, The present ages of two brothers are 15 years and 22 years respectively. Let the required years be represented by x years. According to the question, The product of their age…

Question: The product of the present ages of two sisters is 150. 5 years ago, the elder sister was twice as old as her younger sister. Find their present ages. Solution: Let the present ages of the two sisters be x and y years respectively. According to the question, Condition I, The product of their ages is 150. $or, xy = 150$ - (i…

Question: The difference of the ages of a sister and her younger brother is 6 years. The numerical value of the product of their ages is equal 4 times the sum of their ages. Find the present ages of the sister and her brother. Solution: Let the present ages of the sister and her younger brother be x years and y years respectively. A…

Question: The difference of the ages of two brothers is 4 years. 5 years ago, if the product of their ages was 96, find their present ages. Solution: Let the age of the elder brother before 5 years be x years and that of the younger brother be y years. According to the question, Condition I, The difference of their ages is 4 years. …

Question: The sum of the present ages of elder and younger brothers is 46 years and the product of their ages is 504. Find their present ages. Solution: Let the present ages of two brothers be x years and y years, respectively. Let x years be the age of elder brother. According to the question, Condition I, The sum of their present …

Question: The difference of the present ages of two sisters is 5 years. If the product of their ages is 204, find the age of two sisters. Solution: Let the present ages of one sister be x years and that of the other be y years. According to the question, Condition I, The difference of their present ages is 5 years. $or, x - y = 5$ -…

Question: The square of the sum of the digits in a two-digit number is 64. If 3 is added to four times the number, the digits are reversed. Find the number. Solution: Let the digit at tens place of a two-digit number be x and that at ones place be y. So, the number is 10x +y. According to the question, Condition I, The square of the…

Question: The product of digits in a two-digit number is 18. The number formed by interchanging the digits of the number will be 27 more than the original number. Find the original number. Solution: Let the digit at tens place be x and that at ones place be y. Then, the two-digit number is 10x +y. According to the question, Conditio…

Question: A two-digit number is four times the sum and there times the product of its digits. Find the number. Solution: Let the digit at tens place be x and the digit at ones place be y. So, the two-digit number is 10x +y. According to the question, Condition I, The number is four times the sum of its digits. $or, 10x + y = 4(x +y)…

Question: A two-digit number is such that the product of the digits is 24. When 45 is added to the number, the digits interchange their places. Find the number. Solution: Let the digit at tens place be x and the digit at ones place be y. So, the two-digit number is 10x +y. According to the question, Condition I, The product of its d…

Question: In a two-digit number, the product of the digits is 18 and the sum is 9. Find the number. Solution: Let the number at tens place of a two-digit number be x and that at ones place be y. So, the two-digit number is 10x +y. According to the question, Condition I, The product of the digits is 18. $or, xy = 18$ - (i) Condition …

Question: Find a number which is when added to its square the sum will be 72. Solution: Let the required number be x. According to the question, When x is added to its square (x²), the sum will be 72. $or, x^2 + x = 72$ $or, x^2 + x -72 = 0$ $or, x^2 +(9-8)x -72 = 0$ $or, x^2 +9x -8x -72 = 0$ $or, x(x +9) -8(x +9) = 0$ $or, (x -8)(x…