The difference of two numbers is 1564. After dividing the larger number by the smaller, we get 6 as quotient and 19 as remainder. What is the smaller number?
A. 456
B. 287
C. 623
D. 309
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let two numbers}} = a{\text{ and }}b \cr & a > b \cr & a - b = 1564{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & 6b + 19 = a \cr & a - 6b = 19{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{From equation }}\left( {\text{i}} \right){\text{ and }}\left( {{\text{ii}}} \right) \cr & a - b = 1564 \cr & a - 6b = 19 \cr & - \,\,\,\,\, + \,\,\,\,\, - \cr & \overline {\,\,\,\,\,\,\,5b = 1545\,} \cr & b = 309 \cr & {\text{Smaller number}} = 309 \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
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