A two digit number is obtained by multiplying the sum of the digits by 8. Also, it is obtained by multiplying the difference of the digits by 14 and adding 2. Find the number.

Let x be the digit at ten's place and y be the digit at unit's place. Number = 10(x) + y = 10x + y Given, Number is obtained by multiplying the sum of the digits by 8. ∴ 8(x + y) = 10x + y ⇒ 8x + 8y = 10x + y ⇒ 10x - 8x = 8y - y ⇒ 2x = 7y ⇒ x = y ..........(1) Number is obtained by multiplying the difference of the digits by 14 and adding 2. ⇒ 14(x - y) + 2 = 10x + y .............(2) or, ⇒ 14(y - x) + 2 = 10x + y .............(3) Solving equation (2), ⇒ 14x - 14y + 2 = 10x + y ⇒ 14x - 10x = y + 14y - 2 ⇒ 4x = 15y - 2 ...........(4) Substituting value of x from equation (1) in equation (4), we get : Substituting value of y in equation (1), we get : = 7. Number = 10x + y = 10(7) + 2 = 70 + 2 = 72. Solving equation (3), ⇒ 14(y - x) + 2 = 10x + y ⇒ 14y - 14x + 2 = 10x + y ⇒ 14y - y = 10x + 14x - 2 ⇒ 13y = 24x + 2 ............(5) Substituting value of x from equation (1) in equation (5), we get : This is not possible as y cannot be a fraction. Hence, number = 72.

Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is 4; find the number.

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The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 3, find the number.

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Two articles A and B are sold for ₹ 1,167 making 5% profit on A and 7% profit on B. If the two articles are sold for ₹ 1,165 a profit of 7% is made on A and a profit of 5% is made on B. Find the cost price of each article.

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Mathematics

A two digit number is obtained by multiplying the sum of the digits by 8. Also, it is obtained by multiplying the difference of the digits by 14 and adding 2. Find the number.

Linear Equations

Related Questions

Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is 4; find the number.

The sum of a two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 3, find the number.

Two articles A and B are sold for ₹ 1,167 making 5% profit on A and 7% profit on B. If the two articles are sold for ₹ 1,165 a profit of 7% is made on A and a profit of 5% is made on B. Find the cost price of each article.