.Two natural numbers differ by . If is added to greater number then it becomes equal to twice the smaller number. Those two numbers are: _____, _____.Required to answer. Single choice.
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Let the two numbers be x and y.
It is given that two numbers differ by 7 that is:
x−y=7..........(1)
Also, twice the greater number added to five times the smaller gives 42 that is:
2x+5y=42..........(2).
Multiply the equation 1 by 2:
2x−2y=14..........(3)
Now subtract equation 3 from equation 2 to eliminate x, because the coefficients of x are same. So, we get
(2x−2x)+(5y+2y)=42−14
i.e. 7y=28
i.e. y=4
Substituting this value of y in (1), we get
x−4=7
i.e. x=11
Hence, the two numbers are 11 and 4.
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