Question
24 cubes having sides equal to a cm each, and 24 more cubes
having sides equal to 2a cm each are melted to form a single cube such that diagonal of the new cube formed is 60√3 cm. Find the value of a.Solution
According to the question,
Each side of the bigger cube formed = 60√3/√3 = 60 cm (Diagonal = √3 × side)
Therefore, 24 × (a) 3  + 24 × (2a) 3  = 60 3
Or, 24a 3  × (1 3  + 2 3 ) = (60 × 60 × 60)
Or, 24a 3  (1 + 8) = (60 × 60 × 60)
Or, 216a 3 Â = 60 3
Or a 3 Â = (60/6) 3
Or, a = 10
Simple interest earned on an amount of Rs. 2000 at rate of R% per annum after 4 years is Rs. 288. Find the simple interest earned on an amount of Rs. 15...
Viraj invested Rs. 3500 at 20% p.a. simple interest for 3 years. After 3 years, he invested the amount received by him at the 20% p.a. compound interest...
A sum of Rs. 9,600 earns a simple interest of Rs. 1,920 in 2 years at a certain annual rate. What will be the simple interest on Rs. 12,000 for 4 years ...
A man invested a certain amount of sum at 12.5% per annum simple interest and earned an interest of Rs.2400 after 4 years. If the same amount is investe...
If a sum when placed at compound interest grows to Rs.6,400 in 2 yrs and to Rs. 8,000 in 3 yrs, find the rate percent p.a.
Raju invests a certain amount at an annual simple interest rate of 6% for 2 years. The total amount he receives after this period is then reinvested at ...
Find the total amount returned by Manish to the bank at the end of three years, when Rs.24000 is borrowed at the rate of (25/2)% compounded annually?(ca...
David takes a loan of Rs. 20000 from his friend Alex, which he is to return at 10% p.a. simple interest after 5 years. Alex takes...
A certain sum when invested for 3 years in a scheme offering simple interest of 12% p.a. gives an interest of Rs. 918. What is 122% of the sum invested?
The interest earned on investing Rs. 7000 for 2 years at the rate of 10% p.a., compounded annually, is used to purchase an article. If the article is la...
