Question

In a mathematics class, Raju was requested to add square of the first 10 natural numbers and Rani was
requested to add cubes of the first 10 natural numbers. After the calculation made by Raju and Rani, Ravi was
requested to find the sum of the values obtained by Raju and Rani, Rahim was asked to subtract the sum
obtained by Rani from the sum obtained by Raju. Finally, Roshan was requested to calculate the sum of the
values obtained by Ravi and Rahim. Then what was the sum obtained by Roshan?

Answer 1

Solution :

Raju : 1² + 2² + ....... + 10²

Rani : 1³ + 2³ + ...... + 10³

Ravi : Raju + Rani

=> 1² + 2² + ....... + 10² + 1³ + 2³ + ...... + 10³

Rahim : 1² + 2² + ....... + 10² - ( 1³ + 2³ + ...... + 10³ )

Roshan : Ravi + Rahim

=> 1² + 2² + ....... + 10² + 1³ + 2³ + ...... + 10³ + 1² + 2² + ....... + 10² - ( 1³ + 2³ + ...... + 10³ )

=> 2 [ 1² + 2² + ...... 10² ]

1² + 2² + ..... + 10²

=> n ( n + 1)( 2n + 1)/6 ,

n = 10

=> 10 × 11 × 21/6

=> 5 × 7 × 11

=> 385

Value obtained by roshan :

=> 385 × 2

=> 770

This is the value of the sum of the sum obtained by Roshan.

Thus, this is the required answer .

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