Question : Divide 50 into two parts so that the sum of their reciprocal is $\frac{1}{12}$.
Option 1: 35 and 15
Option 2: 20 and 30
Option 3: 24 and 36
Option 4: 28 and 22
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Correct Answer: 20 and 30
Solution : Given: The number is 50. Let the first part of 50 be $\text{x}$. The second part will be $50 - \text{x}$. The sum of their reciprocal is $\frac{1}{12}$ $\Rightarrow \frac 1 {\text {x} }+ \frac 1 {\text {50-x} }=\frac 1 {\text {12} }$ $\Rightarrow \frac {50+\text {x}-\text {x}} {\text {50x} -{\text{x}^{2}} }=\frac {1}{12}$ $\Rightarrow \text {50x} -{\text{x}^{2}} = 600$ $\Rightarrow \text {50x} -{\text{x}^{2}} - 600=0$ $\Rightarrow {\text{x}^{2}}-\text {50x} + 600=0$ After factorising, we get ⇒ (x-30)(x-20) = 0 ⇒ x = 20 and 30 Hence, the two parts are 20 and 30.
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Question : Two numbers are in the ratio of 2 : 3. If their sum is 125, find the numbers.
Question : The ratio of the ages of two boys is 5 : 6. After two years, the ratio will be 7 : 8. Determine the ratio of their ages after 12 years.
Question : What percentage of 15 hours is 18 seconds?
Question : Directions: After interchanging the given two signs what will be the values of equations (I) and (II) respectively? × and + I. 5 × 12 – 15 + 20 ÷ 25 II. 36 + 3 × 2 – 15 ÷ 5
Question : Directions: Which two signs and two numbers (Not digits) of the equation should be interchanged to make it correct? 13 × 12 ÷ 36 + 11 – 7 = 35
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