Arithmetic Reasoning - Study Mode
[#76] 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
Correct Answer
(C) 45 years
Explanation
Solution: Let 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.
[#77] If you write down all the numbers from 1 to 100, then how many times do you write 3 ?
Correct Answer
(C) 20
Explanation
Solution: Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93
and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39. So, required number = 10 + 10 = 20.
[#78] When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
Correct Answer
(B) 10 years
Explanation
Solution: When Rahul was born, his brother's age = 6 years
His father's age = (6 + 32) years = 38 years, His mother's age = (38 - 3) years = 35 years
His sister's age = (35 - 25) years = 10 years.
[#79] 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 ?
Correct Answer
(D) 20
Explanation
Solution: 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.