Mathematics — Old Questions (TPSC)
Q11. If 50% of x= 3y and 25% of y = 10, then the value of x is :
Given,
50% of x = 3y
25% of y = 10
From second equation:
25% of y = 10
(25 ÷ 100) × y = 10
y = 10 × 100 ÷ 25 = 40
Now substitute y = 40 in first equation:
50% of x = 3 × 40
(50 ÷ 100) × x = 120
x ÷ 2 = 120
x = 240
Answer: The value of x is 240. 📌 Exam tip: Always solve the simpler percentage equation first, then substitute.
Q12. Find the missing number in the series given below: 17, 19, 23, 29, 31, ____, 41, 43, 47.
The given series is:
17, 19, 23, 29, 31, __ , 41, 43, 47
Observe that all the numbers are prime numbers arranged in ascending order.
Prime numbers between 17 and 47 are:
17, 19, 23, 29, 31, 37, 41, 43, 47
So, the missing number is 37.
Answer: The missing number is 37. 📌 Exam tip: If a series contains many primes, first check whether the entire sequence is made of prime numbers.
Q13. Two trains of equal length takes 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross each other traveling in opposite direction?
Length of each train = 120 m
Time taken by first train to cross a post = 10 s
Speed of first train = 120 ÷ 10 = 12 m/s
Time taken by second train to cross a post = 15 s
Speed of second train = 120 ÷ 15 = 8 m/s
Since the trains are moving in opposite directions,
Relative speed = 12 + 8 = 20 m/s
Total distance to be covered to cross each other
= 120 + 120 = 240 m
Time taken = Distance ÷ Relative speed
= 240 ÷ 20 = 12 seconds
Answer: The trains will cross each other in 12 seconds. 📌 Exam tip: For trains moving in opposite directions, add their speeds to get relative speed.
Q14. At the end of a birthday party ,8 persons present in the party shake hands with each other. How many handshakes will there be altogether?
Number of persons present = 8
Each handshake occurs between two persons.
So, total number of handshakes =
n(n − 1) ÷ 2
Here, n = 8
Total handshakes = 8 × 7 ÷ 2
= 28
Answer: Total number of handshakes = 28. 📌 Exam tip: For handshake problems, always use the formula n(n − 1) / 2 — quick and foolproof. Send the next question anytime — I’ll keep giving HTML-ready DB remarks 👍
Q15. The ratio between two numbers is 2:3. If their L.C.M is 150 then the numbers are
Ratio between two numbers = 2 : 3
Let the numbers be 2x and 3x
Since 2 and 3 are co-prime,
L.C.M of the numbers = 2x × 3x = 6x
Given L.C.M = 150
So,
6x = 150
x = 150 ÷ 6 = 25
Therefore,
First number = 2 × 25 = 50
Second number = 3 × 25 = 75
Answer: The numbers are 50 and 75. 📌 Exam tip: When ratio terms are co-prime, LCM = product of the numbers — very useful shortcut.
Q16. A man sold two commodities for Rs. 99 each. On one he gains 10% and on the other he loses 10%. Find his gain or loss percent in the whole transaction.
Selling price of each commodity = Rs. 99
First commodity (10% gain):
Cost Price = 99 × 100 ÷ 110 = 90
Second commodity (10% loss):
Cost Price = 99 × 100 ÷ 90 = 110
Total Cost Price:
90 + 110 = 200
Total Selling Price:
99 + 99 = 198
Loss = 200 − 198 = 2
Loss % = (2 ÷ 200) × 100 = 1%
Answer: There is a 1% loss in the whole transaction. 📌 Exam shortcut: When two articles are sold at the same selling price with equal gain and loss %, the result is always a loss.
Q17. A 150 metres long train takes 20 seconds to cross a 450 meters long platform. The speed of the train in kiolometres per second is:
Length of train = 150 metres
Length of platform = 450 metres
Total distance covered to cross the platform =
150 + 450 = 600 metres
Time taken = 20 seconds
Speed of the train = Distance ÷ Time
= 600 ÷ 20 = 30 metres per second
Convert metres per second to kilometres per second:
30 metres = 30 ÷ 1000 kilometres
= 0.03 kilometres per second
Answer: Speed of the train = 0.03 km per second 📌 Exam note: Always check the unit asked in the question (km/sec, km/hr, m/sec) before finalizing the answer.
Q18. A person covers half of his journey at 15 km/hr and remaining half covers 10 km/hr. What is his average speed for the whole journey?
Half of the journey is covered at 15 km/hr
Remaining half is covered at 10 km/hr
When equal distances are covered at two different speeds,
Average speed = (2 × Speed1 × Speed2) ÷ (Speed1 + Speed2)
So,
Average speed = (2 × 15 × 10) ÷ (15 + 10)
= 300 ÷ 25
= 12 km/hr
Answer: The average speed for the whole journey is 12 km/hr. 📌 Exam shortcut: For equal distances, never take simple average — always use 2ab / (a + b).
Q19. In an examination, a student was asked for to find 5/17 of a certain number. By mistake, he found 5/7 of it. His answer was 150 more than the correct answer. The given number is:
Let the given number be x
Correct value = (5 ÷ 17) × x
Wrong value = (5 ÷ 7) × x
According to the question,
Wrong value − Correct value = 150
So,
(5x ÷ 7) − (5x ÷ 17) = 150
Taking LCM of 7 and 17 = 119
(85x − 35x) ÷ 119 = 150
50x ÷ 119 = 150
50x = 150 × 119
x = (150 × 119) ÷ 50
x = 3 × 119
x = 357
Answer: The given number is 357. 📌 Exam tip: In wrong-calculation problems, always subtract wrong value − correct value to form the equation.
Q20. 1/4 of Nitai's money is equal to 1/6 of Gour's money. If both of them together have Rs.600, what is the difference between their amounts?
Given,
(1 ÷ 4) of Nitai's money = (1 ÷ 6) of Gour's money
Let Nitai's money = N
Let Gour's money = G
So,
N ÷ 4 = G ÷ 6
∴ 6N = 4G
N : G = 2 : 3
Total money = 600
Nitai's money = (2 ÷ 5) × 600 = 240
Gour's money = (3 ÷ 5) × 600 = 360
Difference between their amounts =
360 − 240 = 120
Answer: The difference between their amounts is Rs. 120. 📌 Exam tip: Convert fractional relations into a simple ratio first — fastest approach.