A solid cube, whose diagonal is $$ 128 {\ sqrt {2}} \ cm $$, is molded to form a cuboid. The length and width of the cuboid are 512 cm and 160 cm, respectively. What is the height of the cuboid?

A shopkeeper marks an article 24% above its cost price and allows a 15% discount on the marked price. If he earns a profit of Rs. 27 by selling the article, then the selling price of the article is:

The price of sugar increases by 15%. By what percentage should the consumption of sugar be decreased so that the expenditure on the purchase of sugar remains the same? [Give your answer correct to 2 decimal places.]

Answer the following questions

Nirmal started a business by investing Rs.48000. After 7 months, Vidya joined him with a capital of Rs.56000. At the end of the year of the total profit was Rs.5885. What is the Vidya’s share of the profit?

A certain sum is deposited for 4 years at a rate of 10% per annum on compound interest compounded annually. The difference between ihe interest at the end of 2 years and that at the end of 4 years is ₹5,082. Find the sum (in ₹).

Direction : What value should come in the place of question mark (?) in the following questions?

1798 ÷ 31 × ? = 348

A thief escapes from a police station at 8:00 a.m. on a cycle at a speed of 50 km/h. A policeman starts chasing the thief on a motorbike at 9:30 a.m. at the speed of 65 km/h. At what distance from the police station will the policeman catch up with the thief?

$${3x+4y-2z+9=17},{7x+2y+11z+8=23}$$ and $$ {5x+9y+6z-4=18}$$ then what is  the value of $$ {x+y+z-34}$$?