Mathematics — Old Questions (TPSC)
Q21. 3 litres of water is added to 15 litres of alcohol-water solution containing 40% alcohol strength. The strength of alcohol in new solution will be:
Quantity of solution = 15 litres
Alcohol strength = 40%
Quantity of alcohol in the solution =
40% of 15 = (40 ÷ 100) × 15 = 6 litres
Quantity of water added = 3 litres
New quantity of solution = 15 + 3 = 18 litres
Quantity of alcohol remains the same = 6 litres
Strength of alcohol in new solution =
(6 ÷ 18) × 100 = 33.33%
Answer: Strength of alcohol in the new solution = 33⅓%. 📌 Exam tip: When only water is added, alcohol quantity remains unchanged.
Q22. A bag containing only blue, red and green marbles. All but 15 are blue, all but 13 red and all but 22 are green. How many green marbles are there?
Let the number of blue, red and green marbles be B, R and G respectively.
“All but 15 are blue” means:
R + G = 15 ...(1)
“All but 13 are red” means:
B + G = 13 ...(2)
“All but 22 are green” means:
B + R = 22 ...(3)
Add equations (1), (2) and (3):
(R + G) + (B + G) + (B + R) = 15 + 13 + 22
2(B + R + G) = 50
B + R + G = 25
From equation (1):
R + G = 15
So,
G = 25 − (B + R)
But from (3), B + R = 22
G = 25 − 22 = 3
Answer: Number of green marbles = 3. 📌 Exam tip: “All but x” ⇒ sum of the other items = x — convert carefully.
Q23. 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.
Q24. 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.
Q25. 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.
Q26. 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 👍
Q27. 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.
Q28. 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.
Q29. 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.
Q30. 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).