From each of two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is five times as large as the smaller one. What is the ratio of the two numbers?

 

A stockist wants to make some profit by selling oil. He contemplates about various methods. Which of the following would maximise his profit?

$\mathrm{I}$. Sell oil at 20% profit.

$\mathrm{II}.$ Use 800 g of weight instead of 1 kg

$\mathrm{III}.$Mix 20% impurities in oil and selling it at cost price.

$\mathrm{IV}.$Increase the price by 10% and reduce weights by 10%.

$\left(\mathrm{a}\right)$$\mathrm{I} \mathrm{or} \mathrm{III}$

$\left(\mathrm{b}\right) \mathrm{II}$

$\left(\mathrm{c}\right) \mathrm{II} \mathrm{and} \mathrm{IV}$

$\left(\mathrm{d}\right)$ Profits are same

Aamir, on his death bed, keeps half his property for his wife and divides the rest equally among his three sons: Bimar, Cumar and Danger. Some years later, Bimar dies, leaving half his property to his widow and half to his brothers, Cumar and Danger together, sharing equally. When Cumar makes his will, he keeps half his property for his widow and the rest he bequeaths to his younger brother Danger. When Danger dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has $15,75,0000$

What was the worth of the total property? 

Aamir, on his death bed, keeps half his property for his wife and divides the rest equally among his three sons: Bimar, Cumar and Danger. Some years later, Bimar dies, leaving half his property to his widow and half to his brothers, Cumar and Danger together, sharing equally. When Cumar makes his will, he keeps half his property for his widow and the rest he bequeaths to his younger brother Danger. When Danger dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has $15,75,0000$

What was the ratio of the property owned by the widows of the three sons, in the end?

At a bookstore, "MODERN BOOK STORE" is flashed using neon lights. The words are individu- ally flashed at long intervals of $2, 4, 5$. seconds respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again, is:

A train approaches a tunnel $AB$. Inside the tunnel a cat is located at a point that is $2/5th$2/5th the distance$AB$measured from the entrance $A$. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel,$A$, the train catches the cat exactly at the entrance. If the cat moves to the exit $B$, the train catches the cat at exactly the exit.

The speed of the train is greater than the speed of the cat by what order?