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- Question
A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is
Options- A. 23 years
- B. 34 years
- C. 45 years
- D. None of these
- Correct Answer
- 45 years
ExplanationLet x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.Then, woman's age = (10X + y) years; husband's age = (10y + x) years.
Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)
⟺ (9y-9x) = (1/11)(11y + 11x) = (x + y) ⟺ 10x = 8y ⟺ x = (4/5)y
Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.
Arithmetic Reasoning problems
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- 1. In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
Correct Answer: 3
Explanation:
Let d and s represent the number of daughters and sons respectively.Then, we have :
d - 1 = s and 2 (s - 1) = d.
Solving these two equations, we get: d = 4, s = 3.
- 2. In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score?
Options- A. 62
- B. 45
- C. 28
- D. 20 Discuss
Correct Answer: 20
Explanation:
Total runs scored = (36 x 5) = 180.Let the runs scored by E be x.
Then, runs scored by D = x + 5; runs scored by A = x + 8;
runs scored by B = x + x + 5 = 2x + 5;
runs scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x.
So, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120.
Therefore 3x + 120 =180 ⟺ 3X = 60 ⟺ x = 20.
- 3. Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?
Options- A. 7 times
- B. 8 times
- C. 9 times
- D. 11 times Discuss
Correct Answer: 8 times
Explanation:
L.C.M. of 6, 5, 7, 10 and 12 is 420.So, the bells will toll together after every 420 seconds i.e. 7 minutes.
Now, 7 x 8 = 56 and 7 x 9 = 63.
Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.
- 4. The total number of digits used in numbering the pages of a book having 366 pages is
Options- A. 732
- B. 990
- C. 1098
- D. 1305 Discuss
Correct Answer: 990
Explanation:
Total number of digits= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.
- 5. At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party?
Options- A. 60
- B. 65
- C. 90
- D. None of these Discuss
Correct Answer: 60
Explanation:
- 6. The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago?
Options- A. 71 years
- B. 72 years
- C. 74 years
- D. 77 years Discuss
Correct Answer: 71 years
Explanation:
Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.- 7. A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?
Options- A. 3
- B. 20
- C. 39
- D. None of these Discuss
Correct Answer: 3
Explanation:
Since there are socks of only two colours, so two out of any three socks must always be of the same colour.- 8. What is the product of all the numbers in the dial of a telephone?
Options- A. 1,58,480
- B. 1,59,450
- C. 1,59,480
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.- 9. A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C?
Options- A. 9, 46
- B. 9, 50
- C. 10, 46
- D. 10, 50 Discuss
Correct Answer: 9, 50
Explanation:
We have : A = 3B ...(i) andC - 4 = 2 (A - 4) ...(ii)
Also, A + 4 = 31 or A= 31-4 = 27.
Putting A = 27 in (i), we get: B = 9.
Putting A = 27 in (ii), we get C = 50.
- 10. Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born?
Options- A. 32 years, 23 years
- B. 32 years, 29 years
- C. 35 years, 29 years
- D. 35 years, 33 years Discuss
Correct Answer: 32 years, 23 years
Explanation:
When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.
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