Question

4. A positive number is 7 times another number. If 15 is added to both the numbers,
then one of the new number becomes times the other new number. What are the
numbers?
​

Answer 1

QUESTION :

A positive number is 7 times another number. If 15 is added to both the numbers, then one of the new number becomes ⁵/₂ times the other new number. What are the numbers ?

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SOLUTION :

★ Given :-

• A positive number is 7 times of another number.

• If 15 is added to both the numbers, then one of the new number becomes ⁵/₂ times the other new number.

★ To Find :-

• The numbers = ?

❖ Method 1 :-

Suppose,

• The numbers are x and y.

➲ According to first condition,

$\bigstar \: \: \: \: \: \large{ \sf{ \: x = 7y \: \: \: \: \: - - - - - -> (1) }}$

➲ According to second condition,

$\bigstar \: \: \: \: \large{ \sf{ x + 15 = \dfrac{5}{2} (y + 15) \: \: \: - - - - - - > (2)}}$

➲ From eq. (1), putting the value of x in eq. (2) :-

$\bigstar \: \: \sf{x + 15 = \dfrac{5}{2} (y + 15)} \\ \\ \sf{: \implies \: 7y + 15 = \dfrac{5}{2} (y + 15)} \: \\ \\ \sf{: \implies \: 7y + 15 = \dfrac{5 \: (y + 15)}{2} } \\ \\ \sf{: \implies \: 7y+ 15 = \dfrac{5y + 75}{2} } \: \: \: \: \\ \\ \sf{: \implies \:2 \: (7y + 15) = 5y + 75} \\ \\ \sf{: \implies \:14y + 30 = 5y + 75} \: \: \: \\ \\ \sf{: \implies \:14y - 5y = 75 - 30} \: \: \: \\ \\ \sf{: \implies \: 9y = 45} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{: \implies \: y = \dfrac{45}{9} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ \\ \sf{ \large \therefore \: \: \underline{ \: y = 5 \: }} \: \: \: \: \: \: \: \: \: \:$

➲ Putting the value of y in eq. (1) :-

$\: \: \: \bigstar \: \: \: \: \: \sf{ x = 7y} \\ \\ \sf{ : \implies \: x = 7 \times \underline{5}} \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: x = 35 \: }}}$

Hence, the numbers are : 35 and 5.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

❖ Method 2 :-

Suppose,

• One positive number is x.

➲ According to first condition,

• Another number will be 7x.

➲ According to second condition,

$\bigstar \: \: \: \: \large{ \sf{ 7x + 15 = \dfrac{5}{2} (x + 15)}}$

➲ Solving the above equation :-

$\bigstar \: \: \sf{ 7x + 15 = \dfrac{5}{2} (x + 15)} \\ \\ \: \: \: \: \: \: \: \: \: \sf{ : \implies \: 7x + 15 = \dfrac{5(x + 15)}{2}} \: \: \: \: \: \: \\ \\ \sf{ : \implies \: 7x + 15 = \dfrac{5x + 75}{2}} \\ \\ \: \: \sf{ : \implies \: 2(7x + 15) = 5x + 75}\\ \\ \sf{ : \implies \: 14x + 30 = 5x + 75} \\ \\ \sf{ : \implies \: 14x - 5x = 75 - 30} \\ \\ \sf{ : \implies \: 9x = 45} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ : \implies \: x = \dfrac{45}{9}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: x = 5 \: }}} \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\: \: \: \: \: \sf{Another \: \: number = 7x } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \sf{ = 7 \times \underline{5}} \\ \\ \: \: \: \: \sf{= 35}$

Hence, the numbers are : 5 and 35.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

ANSWER :

If a positive number is 7 times another number and when 15 is added to both the numbers, one of the new number becomes times the other new number; then the numbers are 35 and 5.

Answer 2

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