Mathematics — Old Questions (TPSC)
Q51. If selling price of 10 articles is the same as cost price 12 articles, find the gain percentage.
Selling price of 10 articles = Cost price of 12 articles
Assume cost price of 1 article = 1
Cost price of 12 articles = 12
So, selling price of 10 articles = 12
Selling price of 1 article = 12 ÷ 10 = 1.2
Gain per article = 1.2 − 1 = 0.2
Gain % = (0.2 ÷ 1) × 100 = 20%
Q52. The ratio between two numbers is 3:4. If their L.C.M is 600, then the numbers are:
Ratio between two numbers = 3 : 4
Let the numbers be 3x and 4x
Since 3 and 4 are co-prime,
L.C.M of the numbers = 3x × 4x = 12x
Given L.C.M = 600
So, 12x = 600
x = 600 ÷ 12 = 50
Therefore,
First number = 3 × 50 = 150
Second number = 4 × 50 = 200
Answer: The numbers are 150 and 200
Q53. A man sold two commodities for Rs.99 each. On one he gains 10% and the other he loses 10%. Find his gain or loss percent in the whole transaction.
Selling price of each commodity = 99
First commodity (10% gain):
Gain = 10%
So, Cost Price = 99 × 100 ÷ 110 = 90
Second commodity (10% loss):
Loss = 10%
So, Cost Price = 99 × 100 ÷ 90 = 110
Total Cost Price:
90 + 110 = 200
Total Selling Price:
99 + 99 = 198
Loss = 200 − 198 = 2
Loss % = (2 ÷ 200) × 100 = 1%
Answer: There is a 1% loss in the whole transaction.
Q54. A 150 metres long train takes 20 seconds to cross a 450 metres long platform. The speed of the train in kilometres per minute is
Length of train = 150 metres
Length of platform = 450 metres
Total distance covered to cross the platform
= 150 + 450 = 600 metres
Time taken = 20 seconds
Speed = Distance ÷ Time
= 600 ÷ 20 = 30 metres per second
Convert metres per second to kilometres per minute:
30 m/s = 30 × 60 = 1800 metres per minute
= 1.8 kilometres per minute
Answer: Speed of the train = 1.8 km per minute
Q55. 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?
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.
Q56. In how many years, a sum will be double of it at the rate of 10% per annum?
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.
Q57. If A's salary is 15% more than that of B, then how many percent is B's salary less than that of A?
Let B = 100.
Then A = 115 (15% more).
Percentage by which B is less than A
= (15 / 115) × 100
= 13 1/23%
Q58. 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:
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.
Q59. If 3a = 4b and 7b = 8c, find a:b:c ?
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.
Q60. Successive discount of 10% and 10% are equivalent to a single discount of:
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)%.