Welcome, Guest
Mathematics — Old Questions (TPSC)
Correct: 0/10
Wrong: 0/10
Correct
Wrong
Accuracy
0%
Today (June 10, 2026) Daily MCQs: 60 questions — Showing page 2 of 6
Q11. 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?
Correct Option:
B [ 12 km/hr ]
Explanation: Explanation:
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).
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).
Q12. 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.
Q13. 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.
Q14. 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.
Q15. 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.
Q16. 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.
Q17. 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%
Q18. 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.
Q19. 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
Q20. 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.
Correct: 0/10
Wrong: 0/10
Correct
Wrong
Accuracy
0%