Question

7. If 45 is subtracted from twice the greater of two numbers, it results in
the other number. If 21 is subtracted from twice the smaller number, it
results in the greater number. Find the numbers.​

Answer 1

Answer:

Let no be 2x

Other no 2x_45

The number is 54

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Answer 2

Given,

• If 45 is subtracted from twice the greater of two numbers, it results in  the other number.
• If 21 is subtracted from twice the smaller number , it result in the greater number.

To Find,

• The Number

Solution :

$\implies$ Suppose the Greater Number be a

And, Suppose the Smaller Number be b

Therefore,

$\underline{\boxed{\sf{We \ Know \ that :}}}$

$\implies \boxed{\sf{\pink{Dividend = Divisor \times Quotient + Remainder}}}}$

According to the First Condition :

• If 45 is subtracted from twice the greater of two numbers, it results in  the other number.

$\implies \boxed{\sf{b = 2a - 45}}$   1)Equation

According to the Second Condition :

• If 21 is subtracted from twice the smaller number , it result in the greater number.

$\implies \sf{a = 2b - 21}$   2) Equation

║Now Put the Value of b in Second Equation ║

$\implies \sf{a = 2(2a - 45) - 21}$

$\implies \sf{a = 4a - 90 - 21}$

$\implies \sf{a = 4a - 111}$

$\implies \sf{a - 4a = -111}$

$\implies \sf{-3a = -111}$

$\implies \sf{a = \dfrac{-111}{-3}}$

$\implies \boxed{\sf{a = 37}}$

║Now Put the Value of a in First Equation ║

$\implies \sf{b = 2a - 45}$

$\implies \sf{b = 2(37) - 45}$

$\implies \sf{b = 74 - 45}$

$\implies \boxed{\sf{b = 29}}$

Therefore,

$\boxed{\large{\sf{\red{The \ Greater \ Number = a = 37}}}}$

$\boxed{\large{\sf{\red{The \ Smaller \ Number = b = 29}}}}$

$\rule{200}2$