Mathematics — Old Questions (TPSC)
Q1. In what time will a sum of money put at 12.5 % simple interest trebles itself?
Rate of Simple Interest = 12.5% per annum = 1 ÷ 8
For a sum to become trebled,
Total amount = 3P
Interest gained = 3P − P = 2P
Using Simple Interest formula:
RT = 2
So,
T = 2 ÷ (1 ÷ 8)
T = 16 years
Correct Option: (B) 16 years
📌 Quick exam rule: For SI problems, Time = Required interest % ÷ Rate %
Q2. Two trains of length 125 metre and 175 metre are travelling in the same direction at 40 km/h and 22 km/h respectively. In What time will they completely pass each other?
Length of first train = 125 metres
Length of second train = 175 metres
Speed of first train = 40 km/hr
Speed of second train = 22 km/hr
Since both trains are moving in the same direction,
Relative speed = 40 − 22 = 18 km/hr
Convert km/hr to m/s:
18 km/hr = 18 × 5 ÷ 18 = 5 m/s
Total distance to be covered to completely pass each other =
125 + 175 = 300 metres
Time taken = Distance ÷ Relative speed
= 300 ÷ 5 = 60 seconds
Answer: The trains will completely pass each other in 60 seconds.
📌 Exam tip: Same direction → subtract speeds Opposite direction → add speeds
Q3. A, B and C working together can finish a piece of work in 8 days. A alone can do it in 20 days and B alone can do it in 24 days. In how many days will C will alone can do the same work?
A, B and C together can finish the work in 8 days
So, work done by (A + B + C) in 1 day = 1 ÷ 8
A alone can do the work in 20 days
So, work done by A in 1 day = 1 ÷ 20
B alone can do the work in 24 days
So, work done by B in 1 day = 1 ÷ 24
Work done by C in 1 day =
(1 ÷ 8) − (1 ÷ 20) − (1 ÷ 24)
Taking LCM of 8, 20 and 24 = 120
= (15 − 6 − 5) ÷ 120
= 4 ÷ 120
= 1 ÷ 30
So, C alone can do the work in 30 days
Answer: C alone can complete the work in 30 days.
📌 Exam tip: In work problems, always convert days into 1-day work and subtract.
Q4. A trader will loss 12 % if he sells an article for Rs. 2640.00. For how much should he sell it to gain 12 % ?
Selling price at 12% loss = Rs. 2640
Let Cost Price = CP
At 12% loss,
Selling Price = 88% of CP
So,
0.88 × CP = 2640
CP = 2640 ÷ 0.88
CP = 3000
Now, to gain 12%,
Required Selling Price = 112% of CP
= 1.12 × 3000
= Rs. 3360
Answer: To gain 12%, the article should be sold for Rs. 3360.
📌 Exam shortcut: If loss = x%, CP = SP × 100 / (100 − x) If gain = x%, SP = CP × (100 + x) / 100
Q5. 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.
Q6. 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
Q7. 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.
Q8. 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.
Q9. Find the square root of 0.000169 :
Q10. Convert a speed of 10 m/s into km/h :