Mathematics — Old Questions (TPSC)
Q31. A boat is rowed down stream at 35 Km./hr. and up stream at 17 km./hr. Find the speed of the stream.
Speed of stream = (Downstream speed − Upstream speed) / 2
= (35 − 17) / 2
= 18 / 2
= 9 km/hr
Q32. The sum of the two digit number and 40% of the number obtained by reversing its digits is 87.4. If the sum of digits of original number is 11, then find 60% of original number.
Let the number be 10x + y, so the reversed number is 10y + x.
Given: x + y = 11 ... (1)
Also: (10x + y) + 40% of (10y + x) = 87.4
=> (10x + y) + 0.4(10y + x) = 87.4
=> 10x + y + 4y + 0.4x = 87.4
=> 10.4x + 5y = 87.4
Multiply by 5: 52x + 25y = 437 ... (2)
From (1), y = 11 - x. Put in (2):
52x + 25(11 - x) = 437
=> 52x + 275 - 25x = 437
=> 27x = 162 => x = 6, so y = 5
Original number = 65
60% of 65 = (60/100) × 65 = 39
Answer: 39
Q33. 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.
Q34. 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%.
Q35. 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.
Q36. 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.
Q37. 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.
Q38. 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.
Q39. 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).
Q40. 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.