LINEAR EQUATIONS IN ONE AND TWO VARIABLES (CDS)

Total Questions: 41

31. A number consists of two digits, whose sum is 7. If the digits are reversed, the number is increased by 27. The product of digits of the number is [2015 (II) Evening Shift]

Correct Answer: (c) 10
Solution:Let the number be 10x + y .

32. A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was [2015 (I) Morning Shift]

Correct Answer: (a) 12
Solution:Let x be the required number.

33. Consider the following statements [2015 (I) Morning Shift]

I. The equation 1990x - 173y = has no solution in integers for x and y.
II. The equation 3x - 12y = 7 has no solution in integers for x and y.

Which of the above statement(s) is/are correct?

Correct Answer: (c) Both I and II
Solution:I. Given, 1990x - 173y = 11

34. A certain number of two digits is three times the sum of its digits. If 45 is added to the number, then the digits will be reversed. What is the sum of the squares of the two digits of the number ? [2014 (II) Evening Shift ]

Correct Answer: (c) 53
Solution:Let the two digits number be 10x + y.

35. How many pairs of positive integers m and n satisfy the equation 1/m + 4/n = 1/12, where n is an odd integer less than 60 ? [2014 (II) Evening Shift ]

Correct Answer: (d) 3
Solution:Given equation,

36. Two chairs and one table cost ₹700 and 1 chair and 2 tables cost ₹800. If the cost m tables and m chairs is ₹30000, then what is m equal to? [2014 (I) Morning Shift]

Correct Answer: (a) 60
Solution:Let the cost of chair be x and the cost of table be y, then

37. Ravi’s brother is 3 year elder to him. His father was 28 year of age when his sister was born while his mother was 26 yr of age when he was born. If his sister was 4 year of age when his brother was born, the ages of Ravi’s father and mother, respectively when his brother was born, were [2014 (I) Morning Shift]

Correct Answer: (a) 32 year and 23 year
Solution:When Ravi was born his mother's age is 26 yr and his elder brother is 3 yr elder to him.
∴ Mother's age when, brother was born = 26 - 3 = 23year
Ravi's father was 28 year of age when his sister was born and his sister was 4 year of age when his brother was born.
∴ Age of father when brother was born = 28 + 4 = 32year

38. The sum of two positive numbers x and y is 2.5 times their difference. If the product of numbers is 84, then what is the sum of those two numbers? [2014 (I) Morning Shift]

Correct Answer: (d) 20
Solution:According to the question,

39. A positive number, when increased by 10 equals 200 times its reciprocal. What is number? [2014 (I) Morning Shift]

Correct Answer: (b) 10
Solution:Let the positive number be x.

40. The present age of Ravi’s father is 4 times Ravi’s present age. 5 year back, Ravi’s father was seven times as old as Ravi was at that time. What is the present age of Ravi’s father? [2014 (I) Morning Shift]

Correct Answer: (c) 40 year
Solution:Let present age of Ravi be x. ∴ Present age of Ravi’s father = 4x