Question 1
If \(a=\sqrt{7}-\sqrt{3}\) and \(b=\sqrt{5}-\sqrt{2}\), then which of the following is true?
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If \(a=\sqrt{7}-\sqrt{3}\) and \(b=\sqrt{5}-\sqrt{2}\), then which of the following is true?
Evaluate the expression:
\((\frac{1}{4}\div \frac{1}{2})\) \({}\div (\frac{1}{15}+1-\frac{9}{10})\)
The number of red, blue, and green marbles in a bag is in the ratio \(3 : 4 : 6.\) If 20 red marbles, 15 blue marbles, and an unknown number of green marbles are added to the bag, the ratio of red, blue, and green marbles becomes \(4 : 5 : 7.\) Determine the number of green marbles added.
A invests ₹25,000 for 12 months, B invests ₹50,000 for 6 months. What is A's share of ₹30,000 profit?
A and B start a business with capitals in the ratio \(5 : 3.\) After 6 months, A withdraws ₹10,000 and B doubles his investment. If the initial investment of A was ₹50,000, and the total profit after 1 year is ₹84,000, find the profit share of A.
What is the average of all three-digit numbers divisible by 23?
Two containers of the same volume are 40% and 50% full of water, respectively. They are then filled completely with milk. If the contents of both containers are mixed in a larger vessel, what is the percentage of milk in the final mixture?
A stationery shop ordered 6 dozen red pens and some additional dozen blue pens. The price of the red pens per dozen was three times that of the blue ones. When the order was delivered, it was found that the number of dozens of the two colours had been interchanged. This increased the bill by 40%. Find the ratio of the number of dozens of red pens to the number of dozens of blue pens in the original order.
A flower vendor bought 200 flowers for ₹800. 20 flowers withered and became unsellable. At what price per flower should he sell the remaining flowers to earn a profit of 30% on his total cost?
A furniture store sells a dining table for ₹Z, making a 25% profit. During a festive season, they increase the marked price of the same table to ₹1.6Z. They then offer a special discount of 20% on this increased marked price. What will be the percentage profit made by the store during the festive season?