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Mathematics — Old Questions (TPSC)
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Today (August 22, 2026) Daily MCQs: 60 questions — Showing page 5 of 6
Q41. If 3a = 4b and 7b = 8c, find a:b:c ?
Correct Option:
C [ 32 : 24 : 21 ]
Explanation: Explanation:
Given,
3a = 4b ...(1)
7b = 8c ...(2)
From (1):
a : b = 4 : 3
From (2):
b : c = 8 : 7
To combine the ratios, make b common:
LCM of 3 and 8 = 24
Multiply a : b = 4 : 3 by 8:
a : b = 32 : 24
Multiply b : c = 8 : 7 by 3:
b : c = 24 : 21
So,
a : b : c = 32 : 24 : 21
Answer: a : b : c = 32 : 24 : 21 📌 Exam tip: When two ratios share a common term, equalize the middle term to combine them.
Given,
3a = 4b ...(1)
7b = 8c ...(2)
From (1):
a : b = 4 : 3
From (2):
b : c = 8 : 7
To combine the ratios, make b common:
LCM of 3 and 8 = 24
Multiply a : b = 4 : 3 by 8:
a : b = 32 : 24
Multiply b : c = 8 : 7 by 3:
b : c = 24 : 21
So,
a : b : c = 32 : 24 : 21
Answer: a : b : c = 32 : 24 : 21 📌 Exam tip: When two ratios share a common term, equalize the middle term to combine them.
Q42. Successive discount of 10% and 10% are equivalent to a single discount of:
Correct Option:
D [ 19% ]
Explanation: Explanation:
Successive discounts = 10% and 10%
Formula for equivalent single discount:
Single discount = a + b − (ab ÷ 100)
Here,
a = 10 and b = 10
Single discount = 10 + 10 − (10 × 10 ÷ 100)
= 20 − 1
= 19%
Answer: Equivalent single discount = 19% 📌 Exam shortcut: Two equal successive discounts of x% ⇒ single discount = (2x − x²/100)%.
Successive discounts = 10% and 10%
Formula for equivalent single discount:
Single discount = a + b − (ab ÷ 100)
Here,
a = 10 and b = 10
Single discount = 10 + 10 − (10 × 10 ÷ 100)
= 20 − 1
= 19%
Answer: Equivalent single discount = 19% 📌 Exam shortcut: Two equal successive discounts of x% ⇒ single discount = (2x − x²/100)%.
Q43. Two numbers are in the ratio 2:9. If 10 be added to each, they are in the ratio of 3:10. The numbers are
Correct Option:
A [ 20 and 90 ]
Explanation: Explanation:
Ratio of two numbers = 2 : 9
Let the numbers be 2x and 9x
After adding 10 to each number,
New numbers = (2x + 10) and (9x + 10)
Given new ratio = 3 : 10
So,
(2x + 10) ÷ (9x + 10) = 3 ÷ 10
Cross-multiplying,
10(2x + 10) = 3(9x + 10)
20x + 100 = 27x + 30
7x = 70
x = 10
Original numbers are:
2x = 20
9x = 90
Answer: The numbers are 20 and 90. ✅ Exam tip: In ratio-change problems, always form the equation after the change, not before.
Ratio of two numbers = 2 : 9
Let the numbers be 2x and 9x
After adding 10 to each number,
New numbers = (2x + 10) and (9x + 10)
Given new ratio = 3 : 10
So,
(2x + 10) ÷ (9x + 10) = 3 ÷ 10
Cross-multiplying,
10(2x + 10) = 3(9x + 10)
20x + 100 = 27x + 30
7x = 70
x = 10
Original numbers are:
2x = 20
9x = 90
Answer: The numbers are 20 and 90. ✅ Exam tip: In ratio-change problems, always form the equation after the change, not before.
Q44. The average of first 10 natural numbers is :
Correct Option:
C [ 5.5 ]
Explanation: Explanation:
First 10 natural numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Sum of first 10 natural numbers =
(10 × 11) ÷ 2 = 55
Average = Sum ÷ Number of terms
= 55 ÷ 10 = 5.5
Answer: The average of the first 10 natural numbers is 5.5. 📌 Exam shortcut: Average of first n natural numbers = (n + 1) ÷ 2
First 10 natural numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Sum of first 10 natural numbers =
(10 × 11) ÷ 2 = 55
Average = Sum ÷ Number of terms
= 55 ÷ 10 = 5.5
Answer: The average of the first 10 natural numbers is 5.5. 📌 Exam shortcut: Average of first n natural numbers = (n + 1) ÷ 2
Q45. 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:
Correct Option:
B [ 33*1/3 ]
Explanation: Explanation:
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.
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.
Q46. 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?
Correct Option:
C [ 3 ]
Explanation: Explanation:
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.
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.
Q47. If 50% of x= 3y and 25% of y = 10, then the value of x is :
Correct Option:
C [ 240 ]
Explanation: Explanation:
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.
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.
Q48. Find the missing number in the series given below: 17, 19, 23, 29, 31, ____, 41, 43, 47.
Correct Option:
B [ 37 ]
Explanation: Explanation:
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.
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.
Q49. 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?
Correct Option:
D [ 12 seconds ]
Explanation: Explanation:
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.
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.
Q50. 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?
Correct Option:
C [ 28 ]
Explanation: Explanation:
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 👍
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 👍
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