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09 May 2022, 07:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
82% (02:27) correct
18%
(02:34)
wrong
based on 114
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If the two digits of the age of Mr Manoj are reversed then the new age so obtained is the age of his wife. 1/11 of the sum of their ages is equal to the difference between their ages. If Mr Manoj is older than his wife then find the difference between their ages.
(A) 6 years
(B) 7 years
(C) 8 years
(D) 9 years
(E) 10 years
(A) 6 years
(B) 7 years
(C) 8 years
(D) 9 years
(E) 10 years
09 May 2022, 09:56
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Let x and y be the tens and unit digits in Mr. Manoj's age. Then, the algebraic expression for Mr Manoj's age is 10x + y and for his wife, it will be 10y + x (as it is the reverse of Mr. Manoj).
Then,
[1][/11] (10x + y + 10y + x) = (10x+y) - (10y -x ), or
[1][/11] (11x + 11y) = 9x - 9y, or
x + y = 9x - 9y, or
10y = 8x.
The only positive single-digit integer values for x and y to satisfy the equation would be y = 4 and x = 5.
Therefore, Mr. Manoj's age is 54 and his wife's age is 45. Hence, the difference between their age will be 9 years (Option D)
Then,
[1][/11] (10x + y + 10y + x) = (10x+y) - (10y -x ), or
[1][/11] (11x + 11y) = 9x - 9y, or
x + y = 9x - 9y, or
10y = 8x.
The only positive single-digit integer values for x and y to satisfy the equation would be y = 4 and x = 5.
Therefore, Mr. Manoj's age is 54 and his wife's age is 45. Hence, the difference between their age will be 9 years (Option D)
09 May 2022, 10:01
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Bunuel
\(H = 10a\) + b ; \(W = 10b + a\)
Or, \(\frac{10a + b + 10b + a}{11} = 10a + b - 10b - a\)
Or, \(\frac{11a + 11b}{11} = 9a - 9b\)
Or, \(a + b = 9a - 9b\)
Or, \(10b = 8a\)
Or, \(b = \frac{4a}{5}\)
So, If \(a = 5\) , \(b =4\)
Thus, \(H = 54\) & \(W = 45\) ; Hence, \(H - W = 54 - 45 =>9\), Answer must be (D)
