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Mathematics — Old Questions (TPSC)
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Today (May 21, 2026) Daily MCQs: 60 questions — Showing page 4 of 6
Q31. 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:
Correct Option:
D [ 357 ]
Explanation: Explanation:
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.
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.
Q32. 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?
Correct Option:
A [ Rs. 120 ]
Explanation: Explanation:
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.
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.
Q33. 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.
Q34. 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.
Q35. 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.
Q36. 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%
Q37. 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.
Q38. 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
Q39. 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.
Q40. 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.
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