Quantitative Ab...

Two trains A and B, having speeds in the ratio 3 : 4, start from two different cities 500 km apart. At 9 PM, train A interchanged its speed with train B such that they both reached their destination at the same time. How much distance did train A travel from the beginning of the journey till 9 PM?

A worker is hired for 7 days on the condition that he has to come to work for at least 5 days (it doesn’t matter whether he works for full-day or half-day). He will be given one gold coin for full-day work, one silver coin for half-day work and no coin for being absent. The coins given on different days will have the dates imprinted on them. How many different combinations of gold and silver coins can he accumulate?

In a class, the number of girls was 25% more than the number of boys. Some students joined the class this year in which the ratio of boys and girls was 2 : 3. After the new additions, the total number of girls is 27.27% more than the total number of boys. What is the percentage increase in the number of students after the new additions?

If ‘X’ is a prime number such that 15! + 1 < X < 15! + 15. Then find out the sum of all values that ‘X’ can assume?

A three-digit even number is chosen from a group of all three-digit even numbers. If the probability that the chosen number has all its digits distinct can be written in lowest form as x/y , what is the value of (x + y)(x + y)?

In a rectangle ABCD where AB = 24 cm and BC = 9 cm. Points E and F are midpoints of side AB and CD. A circle is drawn in such a way that its centre coincides with rectangle’s centre. Find out the length of the diameter of the circle if both the lines DE and BF are tangents to the circle?

A square PQRS has side of length 5 cm and points T and U lie outside the square such that TQ = US = 3cm and PT = UR = 4cm. Find the value of UT ?

Find the number of integer values of \(x\) for which \(\frac{x^{2}+3 x-28}{x^{2}+6 x+10}<0 ?\)

A trader mixes two varieties of rice-one at Rs.30 per kg and another at Rs.40 per kg, in the ratio 2 : 3. He uses a false weight which displays 1 Kg while weighing 800 g. What price should he quote to the customers while selling the mixture to have an overall gain of 30%?

Bronze is an alloy which contains copper, zinc and tin in the ratio 20 : 1 : 4. Brass is an alloy of copper and zinc. A mixture of brass and bronze in a certain ratio contains 74% of copper, 16% of zinc and 10% of tin. What is the ratio of copper and zinc in brass?