Mathematics — Old Questions (TPSC)
Q1. P can do a piece of work in 10 days and Q can do the same work in 20 days, with the help of R they can finish the work in 5 days. How many days will it take for R alone to finish the work?
Let the total work be 1 unit.
P can do the work in 10 days,
so P’s one-day work = 1/10.
Q can do the work in 20 days,
so Q’s one-day work = 1/20.
Work done by P and Q together in one day
= 1/10 + 1/20 = 3/20.
Given that P, Q and R together finish the work in 5 days,
so their one-day work = 1/5 = 4/20.
Therefore, R’s one-day work
= (P + Q + R) − (P + Q)
= 4/20 − 3/20 = 1/20.
So, R alone can finish the work in 20 days.
Q2. A train, moving with uniform velocity, crosses a pole in 15 second, while it crosses 100 metre long platform in 25 seconds. The length of the train is:
Let the length of the train be x metres.
Speed of train = x / 15 m/s (crossing a pole).
While crossing a 100 m platform, distance = x + 100 and time = 25 s.
So speed = (x + 100) / 25 m/s.
Since speed is same:
x / 15 = (x + 100) / 25
⇒ 25x = 15x + 1500
⇒ 10x = 1500
⇒ x = 150 metres
Q3. The sum of two numbers is 14 and their difference is 10. Find the product of the two numbers.
Let the numbers be x and y.
Given x + y = 14 and x − y = 10.
Adding both equations: 2x = 24 ⇒ x = 12.
Then y = 14 − 12 = 2.
Product = 12 × 2 = 24
Q4. 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?
Since equal distances are covered, use average speed formula:
Average speed = (2ab)/(a + b).
= (2 × 15 × 10) / (15 + 10)
= 300 / 25 = 12 km/hr
Q5. If 4/5 of an estate be worth Rs. 16800, then what is the value of 3/7 of the estate?
4/5 of estate = Rs. 16800.
Total estate = 16800 × (5/4) = Rs. 21000.
Value of 3/7 of estate = (3/7) × 21000 = Rs. 9000
Q6. A student has to secure 40% marks in a paper to pass. He gets 40 and fails by 40 marks. Find the maximum marks of the paper.
Let maximum marks be x.
Pass marks = 40% of x = 0.40x.
Student scored 40 and failed by 40 marks, so pass marks = 40 + 40 = 80.
Therefore 0.40x = 80 ⇒ x = 200.
Q7. In an examination, a student was asked for to find 3/14 of a certain number. By mistake, he found 3/4 of it. His answer was 150 more than the correct answer. The given number is:
Let the number be x.
Wrong value = (3/4)x and correct value = (3/14)x.
Given (3/4)x − (3/14)x = 150.
⇒ (21 − 6)x / 28 = 150.
⇒ (15/28)x = 150.
⇒ x = 280
Q8. A, B, and C working together can finish a piece of work in 8 days. A alone can do it in 20 days and B alone can do it in 24 days. In how many days will C alone can do the same work?
Let total work = 1 unit.
A’s rate = 1/20 and B’s rate = 1/24.
So (A + B) rate = 11/120.
Given (A + B + C) rate = 1/8 = 15/120.
Therefore C’s rate = 15/120 − 11/120 = 4/120 = 1/30.
Hence C alone can do the work in 30 days
Q9. The average of 10 numbers is calculated as 25. It is discovered later on that while calculating the average, one number, namely 36 was wrongly read as 56. The correct average is:
Average of 10 numbers = 25
Wrong total = 25 × 10 = 250
One number 36 was wrongly taken as 56
Excess added = 56 − 36 = 20
Correct total = 250 − 20 = 230
Correct average = 230 ÷ 10 = 23
Q10. 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%