| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] A two-digit number is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of digits by 13 and adding 2. The number is 41. |
| Reason [R] The linear equations used are \[7x-2y+1=0\] and\[12x-23y+2=0\]. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: C
Solution :
| Let the digit at units place be x and the digit at ten's place be y. Then, number \[=10y+x\] |
| According to the given condition, we have |
| \[10y+x=8\left( x+y \right)+1\Rightarrow 7x-2y+1=0\] ... (i) |
| and, \[10y+x=13\left( y-x \right)+2\] |
| \[\Rightarrow \,\,\,14x-3y-2=0\] ... (ii) |
| On multiplying Eq. (i) by 2, we get |
| \[14x-4y+2=0\] ... (iii) |
| On subtracting Eq. (iii) from Eq. (ii), we get |
| \[y-4=0\,\,\Rightarrow \,\,y=4\] |
| From Eq. (i) |
| \[7x-2\left( 4 \right)+1=0\] |
| \[\Rightarrow \,\,\,7x-8+1=0\] |
| \[\Rightarrow \,\,\,7x-7=0\] |
| \[\Rightarrow \,\,\,7x=7\] |
| \[\Rightarrow \,\,\,x=1\] |
| Hence, the number \[=10y+x\] |
| \[=10\times 4+1=41\] |
| Assertion : True; Reason : False |
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