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Mathematics — Old Questions (TPSC)
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Today (February 05, 2026) Daily MCQs: 60 questions — Showing page 1 of 6
Q1. 1/3 of Samir's money is equal to 1/2 of Rahul's money. If both of them together have Rs.500, what is the difference between their amounts?
Correct Option:
C [ Rs. 100 ]
Explanation: Explanation:
Given,
(1 ÷ 3) of Samir's money = (1 ÷ 2) of Rahul's money
Let Samir's money = S
Let Rahul's money = R
So,
S ÷ 3 = R ÷ 2
∴ 2S = 3R
Ratio of Samir's and Rahul's money = 3 : 2
Total money = 500
Samir's money = (3 ÷ 5) × 500 = 300
Rahul's money = (2 ÷ 5) × 500 = 200
Difference between their amounts = 300 − 200 = 100
Answer: Difference between their amounts = Rs. 100 📌 Exam tip: Convert fractional relations into a ratio first — saves time and avoids mistakes.
Given,
(1 ÷ 3) of Samir's money = (1 ÷ 2) of Rahul's money
Let Samir's money = S
Let Rahul's money = R
So,
S ÷ 3 = R ÷ 2
∴ 2S = 3R
Ratio of Samir's and Rahul's money = 3 : 2
Total money = 500
Samir's money = (3 ÷ 5) × 500 = 300
Rahul's money = (2 ÷ 5) × 500 = 200
Difference between their amounts = 300 − 200 = 100
Answer: Difference between their amounts = Rs. 100 📌 Exam tip: Convert fractional relations into a ratio first — saves time and avoids mistakes.
Q2. In how many years, a sum will be double of it at the rate of 10% per annum?
Correct Option:
A [ 10 years ]
Explanation: Explanation:
Rate of interest = 10% per annum
For a sum to become double,
Gain required = 100% of the principal
Using Simple Interest formula:
Time = (Gain % ÷ Rate %)
Time = 100 ÷ 10 = 10 years
Answer: The sum will become double in 10 years.
Rate of interest = 10% per annum
For a sum to become double,
Gain required = 100% of the principal
Using Simple Interest formula:
Time = (Gain % ÷ Rate %)
Time = 100 ÷ 10 = 10 years
Answer: The sum will become double in 10 years.
Q3. If A's salary is 15% more than that of B, then how many percent is B's salary less than that of A?
Correct Option:
B [ 13*1/23 ]
Explanation: Logic:
Let B = 100.
Then A = 115 (15% more).
Percentage by which B is less than A
= (15 / 115) × 100
= 13 1/23%
Let B = 100.
Then A = 115 (15% more).
Percentage by which B is less than A
= (15 / 115) × 100
= 13 1/23%
Q4. The ration between two numbers is 3:4. If each number is increased by 6, the ratio becomes 4:5. The difference between the numbers is:
Correct Option:
A [ 6 ]
Explanation: Explanation:
Ratio of two numbers = 3 : 4
Let the numbers be 3x and 4x
After increasing each number by 6,
New numbers = (3x + 6) and (4x + 6)
Given new ratio = 4 : 5
So,
(3x + 6) ÷ (4x + 6) = 4 ÷ 5
Cross-multiplying,
5(3x + 6) = 4(4x + 6)
15x + 30 = 16x + 24
x = 6
Original numbers are:
3x = 18
4x = 24
Difference between the numbers = 24 − 18 = 6
Answer: The difference between the numbers is 6.
Ratio of two numbers = 3 : 4
Let the numbers be 3x and 4x
After increasing each number by 6,
New numbers = (3x + 6) and (4x + 6)
Given new ratio = 4 : 5
So,
(3x + 6) ÷ (4x + 6) = 4 ÷ 5
Cross-multiplying,
5(3x + 6) = 4(4x + 6)
15x + 30 = 16x + 24
x = 6
Original numbers are:
3x = 18
4x = 24
Difference between the numbers = 24 − 18 = 6
Answer: The difference between the numbers is 6.
Q5. 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.
Q6. 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)%.
Q7. 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.
Q8. 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
Q9. 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.
Q10. 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.
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