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Mathematics — Old Questions (TPSC)
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Today (February 05, 2026) Daily MCQs: 60 questions — Showing page 3 of 6
Q21. The rate of simple interest being 10% per annum, in how many years, a sum will be thrice of it?
Correct Option:
B [ 20 years ]
Explanation: Explanation:
Rate of simple interest = 10% per annum
For a sum to become thrice,
Total amount = 3P
So, Interest gained = 3P − P = 2P
Interest required = 200% of principal
Using Simple Interest formula:
Time = (Interest % ÷ Rate %)
Time = 200 ÷ 10 = 20 years
Answer: The sum will become thrice in 20 years. 📌 Exam note: In Simple Interest, amount increases linearly, so convert change into percentage of principal.
Rate of simple interest = 10% per annum
For a sum to become thrice,
Total amount = 3P
So, Interest gained = 3P − P = 2P
Interest required = 200% of principal
Using Simple Interest formula:
Time = (Interest % ÷ Rate %)
Time = 200 ÷ 10 = 20 years
Answer: The sum will become thrice in 20 years. 📌 Exam note: In Simple Interest, amount increases linearly, so convert change into percentage of principal.
Q22. If salary of A is 20% more than that of B, then B's salary is less than that of A by?
Correct Option:
D [ 16*2/3 % ]
Explanation: Explanation:
Let B's salary = 100
Salary of A is 20% more than B
So, A's salary = 120
Difference = 120 − 100 = 20
Percentage by which B is less than A =
(20 ÷ 120) × 100
= 16.66%
= 16⅔%
Answer: B's salary is less than A's by 16⅔%. 📌 Exam tip:
When comparison base changes, percentage also changes — never use the same % both ways.
Let B's salary = 100
Salary of A is 20% more than B
So, A's salary = 120
Difference = 120 − 100 = 20
Percentage by which B is less than A =
(20 ÷ 120) × 100
= 16.66%
= 16⅔%
Answer: B's salary is less than A's by 16⅔%. 📌 Exam tip:
When comparison base changes, percentage also changes — never use the same % both ways.
Q23. If 4a = 5b and 8b = 9c, find a:b:c ?
Correct Option:
A [ 45 : 36 : 32 ]
Explanation: Explanation:
Given,
4a = 5b ...(1)
8b = 9c ...(2)
From (1):
a : b = 5 : 4
From (2):
b : c = 9 : 8
To combine the ratios, make b common:
LCM of 4 and 9 = 36
Multiply a : b = 5 : 4 by 9:
a : b = 45 : 36
Multiply b : c = 9 : 8 by 4:
b : c = 36 : 32
So,
a : b : c = 45 : 36 : 32
Answer: a : b : c = 45 : 36 : 32 📌 Exam tip: When two equations give linked ratios, equalize the middle term to get the combined ratio.
Given,
4a = 5b ...(1)
8b = 9c ...(2)
From (1):
a : b = 5 : 4
From (2):
b : c = 9 : 8
To combine the ratios, make b common:
LCM of 4 and 9 = 36
Multiply a : b = 5 : 4 by 9:
a : b = 45 : 36
Multiply b : c = 9 : 8 by 4:
b : c = 36 : 32
So,
a : b : c = 45 : 36 : 32
Answer: a : b : c = 45 : 36 : 32 📌 Exam tip: When two equations give linked ratios, equalize the middle term to get the combined ratio.
Q24. The length of rectangle is increased by 10% and breadth decreased by 10% then the area of the new rectangle is:
Correct Option:
A [ Decreased by 1% ]
Explanation: Explanation:
Let original length = L
Let original breadth = B
Original area = L × B
New length = L + 10% of L = 1.1L
New breadth = B − 10% of B = 0.9B
New area = 1.1L × 0.9B
= 0.99LB
Change in area = 0.99LB − LB = −0.01LB
Percentage change in area =
(0.01LB ÷ LB) × 100 = 1% decrease
Answer: The area of the new rectangle is 1% less than the original area.
📌 Exam shortcut: For small % changes, Net % change = a + b + (ab ÷ 100) Here → 10 − 10 − 1 = −1%
Let original length = L
Let original breadth = B
Original area = L × B
New length = L + 10% of L = 1.1L
New breadth = B − 10% of B = 0.9B
New area = 1.1L × 0.9B
= 0.99LB
Change in area = 0.99LB − LB = −0.01LB
Percentage change in area =
(0.01LB ÷ LB) × 100 = 1% decrease
Answer: The area of the new rectangle is 1% less than the original area.
📌 Exam shortcut: For small % changes, Net % change = a + b + (ab ÷ 100) Here → 10 − 10 − 1 = −1%
Q25. If 20 workers can earn wages Rs.20,000 in 5 days, earning of 12 workers in 10 days will be:
Correct Option:
B [ Rs.24,000 ]
Explanation: Explanation:
Number of workers = 20
Number of days = 5
Total wages = Rs. 20,000
Earning per worker per day =
20000 ÷ (20 × 5) = 200
Now,
Number of workers = 12
Number of days = 10
Total earning = 12 × 10 × 200
= Rs. 24,000
Answer: Earning of 12 workers in 10 days = Rs. 24,000.
📌 Exam tip: In wage problems, always find per worker per day earning first — safest and fastest method.
Number of workers = 20
Number of days = 5
Total wages = Rs. 20,000
Earning per worker per day =
20000 ÷ (20 × 5) = 200
Now,
Number of workers = 12
Number of days = 10
Total earning = 12 × 10 × 200
= Rs. 24,000
Answer: Earning of 12 workers in 10 days = Rs. 24,000.
📌 Exam tip: In wage problems, always find per worker per day earning first — safest and fastest method.
Q26. A piece of cloth was purchased by Rs.600. To earn 9.5% profit the sale price will be:
Correct Option:
B [ Rs.657.00 ]
Explanation: Explanation:
Cost Price (CP) = Rs. 600
Profit = 9.5%
Profit amount = 9.5% of 600
= (9.5 ÷ 100) × 600
= 57
Selling Price (SP) = CP + Profit
= 600 + 57
= Rs. 657
Answer: To earn 9.5% profit, the selling price will be Rs. 657.
📌 Exam shortcut: Selling Price = CP × (100 + Profit %) ÷ 100
Cost Price (CP) = Rs. 600
Profit = 9.5%
Profit amount = 9.5% of 600
= (9.5 ÷ 100) × 600
= 57
Selling Price (SP) = CP + Profit
= 600 + 57
= Rs. 657
Answer: To earn 9.5% profit, the selling price will be Rs. 657.
📌 Exam shortcut: Selling Price = CP × (100 + Profit %) ÷ 100
Q27. In one minute 3/7 of a bucket is filled. The rest of the bucket can be fill in:
Correct Option:
C [ 4/3 minutes ]
Explanation: Explanation:
In 1 minute, 3 ÷ 7 of the bucket is filled
So, total time to fill the whole bucket =
1 ÷ (3 ÷ 7) = 7 ÷ 3 minutes
Part already filled = 3 ÷ 7
Remaining part = 1 − (3 ÷ 7) = 4 ÷ 7
Time required to fill the remaining part =
(4 ÷ 7) × (7 ÷ 3)
= 4 ÷ 3 minutes
Correct Option: (C) 4 ÷ 3 minutes
📌 Quick exam logic: Once you know the total time, multiply it by the remaining fraction.
In 1 minute, 3 ÷ 7 of the bucket is filled
So, total time to fill the whole bucket =
1 ÷ (3 ÷ 7) = 7 ÷ 3 minutes
Part already filled = 3 ÷ 7
Remaining part = 1 − (3 ÷ 7) = 4 ÷ 7
Time required to fill the remaining part =
(4 ÷ 7) × (7 ÷ 3)
= 4 ÷ 3 minutes
Correct Option: (C) 4 ÷ 3 minutes
📌 Quick exam logic: Once you know the total time, multiply it by the remaining fraction.
Q28. A man reached at 09.00 hours in a place of meeting on Sunday. He was 10 minutes earlier than the man who was 30 minutes late in attending the meeting. What was the schedule time of meeting?
Correct Option:
B [ 08.40 ]
Explanation: Explanation:
One man reached the meeting place at 09:00 hours
He was 10 minutes earlier than another man
So, the other man reached at = 09:10 hours
This second man was 30 minutes late for the meeting
Therefore, scheduled time of the meeting =
09:10 − 30 minutes = 08:40 hours
Answer: The scheduled time of the meeting was 08:40 hours.
📌 Exam tip: In early–late time problems, always first find the actual arrival time of the late person, then subtract the lateness.
One man reached the meeting place at 09:00 hours
He was 10 minutes earlier than another man
So, the other man reached at = 09:10 hours
This second man was 30 minutes late for the meeting
Therefore, scheduled time of the meeting =
09:10 − 30 minutes = 08:40 hours
Answer: The scheduled time of the meeting was 08:40 hours.
📌 Exam tip: In early–late time problems, always first find the actual arrival time of the late person, then subtract the lateness.
Q29.
Correct Option:
D [ 20% ]
Explanation: Explanation:
Increase in price of petrol = 25%
Let original price = 100
New price = 125
To keep expenditure same,
Price × Consumption must remain constant
Required reduction in consumption =
(Increase ÷ New price) × 100
= (25 ÷ 125) × 100
= 20%
Answer: The car owner must reduce petrol consumption by 20%.
📌 Exam shortcut: If price increases by x%, Required reduction in consumption = x / (100 + x) × 100.
Increase in price of petrol = 25%
Let original price = 100
New price = 125
To keep expenditure same,
Price × Consumption must remain constant
Required reduction in consumption =
(Increase ÷ New price) × 100
= (25 ÷ 125) × 100
= 20%
Answer: The car owner must reduce petrol consumption by 20%.
📌 Exam shortcut: If price increases by x%, Required reduction in consumption = x / (100 + x) × 100.
Q30. A bag contains 25 paise, 10 paise and 5 paise coin in the ratio 1:2:3. If their total value is Rs. 30, then the number of 5 paise coin is:
Correct Option:
C [ 150 ]
Explanation: Explanation:
The bag contains 25 paise, 10 paise and 5 paise coins in the ratio 1 : 2 : 3
Let the numbers of 25p, 10p and 5p coins be:
x, 2x and 3x respectively
Total value of coins = Rs. 30 = 3000 paise
Value of coins:
25p coins = 25 × x = 25x
10p coins = 10 × 2x = 20x
5p coins = 5 × 3x = 15x
Total value = 25x + 20x + 15x = 60x paise
So,
60x = 3000
x = 3000 ÷ 60 = 50
Number of 5 paise coins = 3x = 3 × 50 = 150
Answer: Number of 5 paise coins = 150.
📌 Exam tip: Convert rupees into paise first, then form the value equation — avoids mistakes.
The bag contains 25 paise, 10 paise and 5 paise coins in the ratio 1 : 2 : 3
Let the numbers of 25p, 10p and 5p coins be:
x, 2x and 3x respectively
Total value of coins = Rs. 30 = 3000 paise
Value of coins:
25p coins = 25 × x = 25x
10p coins = 10 × 2x = 20x
5p coins = 5 × 3x = 15x
Total value = 25x + 20x + 15x = 60x paise
So,
60x = 3000
x = 3000 ÷ 60 = 50
Number of 5 paise coins = 3x = 3 × 50 = 150
Answer: Number of 5 paise coins = 150.
📌 Exam tip: Convert rupees into paise first, then form the value equation — avoids mistakes.
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