For the following questions answer them individually
A shopkeeper sold a pair of headphones for ₹5,520 at a gain of 20%. What would have been the gain or loss percent if it had been sold for ₹4,370?
In a certain year, the population of a city was 18000. If in the next year, the population of males increased by 5% and that of females increased by 7%, and the total population increased to 19200, then what was the ratio of the populations of males and females in that given year?
An inlet pipe can fill an empty tank in 120 hours while an outlet pipe drains a completely-filled tank in 54 hours. If 8 inlet pipes and 3 outlet pipes are opened simultaneously, when the tank is empty, then in how many hours will the tank get completely filled?
The marked price of a frock is ₹4,500. It is to be sold at ₹2,400 at two successive discounts. If the first discount is 20%, then the second discount will be:
Two trains of length 130 m and 120 mare running on parallel lines in the same direction at a speed of 40 km/h and 50 km/h, respectively. In how much time will they pass each other?
The square of the sum of two given natural numbers is 784, while the product of the two given numbers is 192. Find the positive difference between the squares of these two given numbers.
Solve the given expression.
$$\frac{\sec^2(90^\circ - \theta) - \cot^2 \theta}{2(\sin^2 35^\circ + \sin^2 55^\circ)}$$
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