Divide 50 into two parts so that the sum of t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the two parts be $x$ and $(50 - x)$.According to the problem,the sum of their reciprocals is $1/12$:$\frac{1}{x} + \frac{1}{50 - x} = \frac{1}

Vedclass · Accepted Answer

$20, 30$

Vedclass · Answer

(A) Let the two parts be $x$ and $(50 - x)$.According to the problem,the sum of their reciprocals is $1/12$:$\frac{1}{x} + \frac{1}{50 - x} = \frac{1}{12}$Taking the common denominator on the left side:$\frac{(50 - x) + x}{x(50 - x)} = \frac{1}{12}$$\frac{50}{50x - x^2} = \frac{1}{12}$Cross-multiplying gives:$50 	imes 12 = 50x - x^2$$600 = 50x - x^2$Rearranging into a standard quadratic equation:$x^2 - 50x + 600 = 0$Factoring the quadratic equation:$(x - 30)(x - 20) = 0$Thus,$x = 30$ or $x = 20$.If $x = 30$,the other part is $50 - 30 = 20$. If $x = 20$,the other part is $50 - 20 = 30$.Therefore,the two parts are $20$ and $30$.

Divide $50$ into two parts so that the sum of their reciprocals is $1/12$.

Similar Questions

$[(3^{2})^{6}]^{5} = 9^{?}$

$6 - \left[ \frac{5}{6} + \left\{ 3 \frac{7}{8} - 2 \frac{1}{3} + 1 \frac{7}{9} \right\} \right] = ?$

In a division sum, the divisor is $10$ times the quotient and $5$ times the remainder. What is the dividend, if the remainder is $46$?

$26.5 \%$ of $488 = ?$

$47 \times 251 - 13343 + 1547 = ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module