Mathematics — Old Questions (TPSC)
Q11. A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71. The number of 25-paise coins is
Let the number of 25-paise coins be x.
Then number of 20-paise coins = 324 − x.
Total value = Rs. 71 = 7100 paise
25x + 20(324 − x) = 7100
=> 25x + 6480 − 20x = 7100
=> 5x = 620
=> x = 124
Since 124 is not in the options, the correct answer is None of these.
Q12. The ratio of cost price and selling price of an article is 20 : 21. Then the profit per cent on it is
Let Cost Price = 20 and Selling Price = 21.
Profit = 21 − 20 = 1.
Profit % = (Profit / Cost Price) × 100
= (1 / 20) × 100
= 5%.
Q13. Rahul is 4 years younger than his elder brother Shyam. Rahul also has a sister who is 3 years younger to him. What is the difference between the age of Rahul and the average age of the three siblings?
Let Rahul = R years.
Shyam = R+4, Sister = R-3.
Average age = (R + (R+4) + (R-3)) / 3 = (3R+1)/3 = R + 1/3.
Difference = 1/3 year = 4 months.
Q14. How many multiples of 3 are there from 1 to 100 which are not multiples of 2?
Multiples of 3 from 1 to 100 = floor(100/3) = 33.
Multiples of both 3 and 2 are multiples of 6: floor(100/6) = 16.
Required = 33 - 16 = 17.
Q15. In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is
Let cows = c, hens = h.
Heads = c + h.
Legs = 4c + 2h.
Given: 4c + 2h = 2(c + h) + 14
=> 4c + 2h = 2c + 2h + 14
=> 2c = 14
=> c = 7.
Q16. A sum of money tripled itself at compound interest in 10 years. In how many years will it become 27 times?
If it becomes 3 times in 10 years, then every 10 years it multiplies by 3 (same rate).
27 = 33 = 3 × 3 × 3.
So time = 3 × 10 = 30 years.
Q17. The sum of 6 consecutive integers is 9. What is the lowest integer?
Let the integers be n, n+1, n+2, n+3, n+4, n+5.
Sum = 6n + 15 = 9
=> 6n = -6
=> n = -1 (lowest integer).
Q18. A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number?
Let number = 10x + y, with x + y = 11.
Reversed = 10y + x.
Given: 10x + y + 27 = 10y + x
=> 9x - 9y = -27
=> x - y = -3
Solving with x+y=11 gives x=4, y=7? (Check) Actually x-y=-3 and x+y=11 => x=4, y=7.
Number = 47, and 47 + 27 = 74 (reversed).
Answer: 47.
Q19. A number when divided by 80 leaves remainder 20. What is the remainder when the same number is divided by 16?
Number N = 80k + 20.
Divide by 16: 80k is divisible by 16 (since 80 = 16×5).
So remainder = 20 mod 16 = 4.
Q20. When the price of sugar decreases by 10%, a man could buy 1 kg more for Rs. 270. Then, the original price of sugar per kg is
Let original price = Rs. P per kg.
New price after 10% decrease = 0.9P.
With Rs.270: quantities are 270/P and 270/(0.9P).
Given difference = 1 kg:
270/(0.9P) - 270/P = 1
270(1/0.9 - 1)/P = 1
270((10/9) - 1)/P = 1
270(1/9)/P = 1
30/P = 1 => P = 30.