Mathematics — Old Questions (TPSC)
Q41. 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.
Q42. 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.
Q43. The least number which must be added to 3931 to make it a perfect square, is
622 = 3844 and 632 = 3969.
3931 lies between them.
3969 − 3931 = 38, so 3931 + 38 = 3969 (a perfect square).
Q44. If x4 + 1/x4 = 527 , then the value of x + 1/x is
x4 + 1/x4 = (x2 + 1/x2)2 − 2.
So (x2 + 1/x2)2 = 529 ⇒ x2 + 1/x2 = 23.
(x + 1/x)2 = 23 + 2 = 25 ⇒ x + 1/x = 5.
Q45. There are five types of envelope and four types of stamps in a Post office. How many ways are there to buy an envelope and a stamp?
Number of ways = (choices of envelope) × (choices of stamp)
= 5 × 4 = 20.
Q46. If x4 + 1/x4 = 527, then the value of x + 1/x is
x4 + 1/x4 = (x2 + 1/x2)2 − 2.
So (x2 + 1/x2)2 = 527 + 2 = 529.
Hence x2 + 1/x2 = 23.
Now (x + 1/x)2 = x2 + 1/x2 + 2 = 23 + 2 = 25.
Therefore x + 1/x = 5.
Answer: 5
Q47. By selling a bicycle for Rs. 2200, a man gains 10%. At what price did he buy the bicycle?
Gain = 10%, Selling Price = Rs. 2200.
Cost Price = (Selling Price × 100) / (100 + Gain%)
= (2200 × 100) / 110 = Rs. 2000
Q48. A number when added to its half gives 63. Find the number.
Let the number be x.
x + x/2 = 63
⇒ (3x)/2 = 63
⇒ x = (63 × 2)/3 = 42
Q49. A sum of money lent at simple interest becomes Rs. 3224.00 in 2 years and Rs. 4160.00 in 5 years. Find out the sum.
Difference of amounts = 4160 − 3224 = 936, which is interest for 3 years.
Yearly interest = 936 ÷ 3 = 312.
Interest for 2 years = 312 × 2 = 624.
Principal = 3224 − 624 = Rs. 2600
Q50. A, B, and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone can do the same work?
A + B + C work rate = 1/8.
A''s rate = 1/20 and B''s rate = 1/24.
C''s rate = 1/8 − (1/20 + 1/24).
= 15/120 − 11/120 = 4/120 = 1/30.
Hence, C alone can do the work in 30 hours