The salaries of three friends Sita, Gita and Mita are initially in the ratio 5:6:7 respectively. In the first year, they get salary hikes of 20%, 25% and 20% , respectively. In the second year, Sita and Mita get salary hikes of 40% and 25% , respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

Question

In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

Answer 1

Initially, the salaries of Sita, Gita, and Mita were in the ratio \(5:6:7\). Let their salaries be \(5p, 6p,\) and \(7p\), respectively. After receiving salary increases of \(20\%\), \(25\%\), and \(20\%\) respectively, their new salaries became \(6p, 7.5p,\) and \(8.4p\). Subsequently, Sita and Mita received further salary hikes of \(40\%\) and \(25\%\), respectively. Sita's salary became \(1.4 \times 6p = 8.4p\), and Mita's salary became \(1.25 \times 8.4p = 10.5p\). Let Gita's salary after her hike be g. The equation \(3g = 8.4p + g + 10.5p\) simplifies to \(2g = 18.9p\), which gives \(g = 9.45p\). The percentage hike for Gita is \(\frac {9.45p — 7.5p}{7.5p} \times 100 = 26\%\).

The answer is \(26\%\).

Solution and Explanation

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