Mathematics — Old Questions (TPSC)
Q51. What is the sum of numbers from 1 to 100?
The sum of numbers from 1 to 100 is the sum of first 100 natural numbers.
Formula for sum of first n natural numbers =
n(n + 1) ÷ 2
Here, n = 100
Sum = 100 × 101 ÷ 2
= 5050
Answer: The sum of numbers from 1 to 100 is 5050.
📌 Exam tip: Always use the formula n(n + 1)/2 for fast calculation.
Q52. The product of two numbers is 7200. If their HCF is 20, then what will be the LCM?
Product of two numbers = 7200
HCF of the two numbers = 20
Relationship between two numbers:
Product of numbers = HCF × LCM
So,
LCM = 7200 ÷ 20
= 360
Answer: The LCM of the two numbers is 360.
📌 Exam tip: Always remember: Number₁ × Number₂ = HCF × LCM
Q53. Four-fifth of a number is greater than three-fourth of that number by 4. the number is :
Let the number be x
Four-fifth of the number = (4 ÷ 5)x
Three-fourth of the number = (3 ÷ 4)x
Given that,
(4 ÷ 5)x is greater than (3 ÷ 4)x by 4
So,
(4 ÷ 5)x − (3 ÷ 4)x = 4
Taking LCM of 5 and 4 = 20
(16x − 15x) ÷ 20 = 4
x ÷ 20 = 4
x = 80
Answer: The number is 80.
📌 Exam tip: Convert fractions to a common denominator first to avoid mistakes.
Q54. The length of a rectangular field is twice its breadth. If the perimeter of the field is 150 metre, find its lenght :
Let breadth of the rectangular field = x metre
Then length of the field = 2x metre
Perimeter of a rectangle = 2(length + breadth)
Given perimeter = 150 metre
So,
2(2x + x) = 150
2(3x) = 150
6x = 150
x = 25
Length of the field = 2x = 2 × 25 = 50 metres
Answer: The length of the field is 50 metres.
📌 Exam tip: Always express length in terms of breadth when a ratio is given.
Q55. Find the square root of 0.000169 :
Q56. Convert a speed of 10 m/s into km/h :
Q57. 96 % of the cost of a TV is Rs. 10,464.00. What is its total cost ?
Q58. If (3a + 7b) : (5a - 3b) = 5:3, a:b will be :
Q59. A sum of money at simple interest doubles itself in 10 years. Find the rate of interest per annum.
Q60. A alone can finish a piece of work in 12 days and B alone can do it in 15 days. How much time will they take to finish this work if they work together ?