Cube of a number-Solution

Question

Solution:
The smallest 10 digit no starts with 1 and is followed by 9 zeroes. When we take the cube of it, we get a 28 digit no.

Also, the smallest 11 digit no. starts with 1 and is followed by 10 zero's. When we take the cube of it, we get a 31 digit no.

Hence, the no. of digits in the cube root of a 29 digit number should be b) 10.

Cube of a number

Question:

The cube of an integer consists of 29 digits. How many digits would the original number have?
a)11 b)10 c)9 d)8 e)cant say


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Simultaneous Equation Solution - 1

QUESTION


Solution:
Total No. of fruits initially in the basket = 11

Avg. Cost per fruit in the basket after replacement = 19.27...

Logic:
Let the no. of pears be A and that of peaches be O.
Let the cost of an pear be x and that of an peach be y.

Total cost = Ax + Oy = 248 .... Given
Avg cost of fruit = (Ax + Oy)/(A + O) = 248/(A + O)

Adding an Pear the equation becomes : (248 + x)/(A + O + 1) = Avg. + 2
Adding an Peach the equation becomes : (248 + y)/(A + O + 1) = Avg. - 1

Subtracting the above equations : (x - y)/ (A + O + 1) = 3
i.e. x-y = 3 (A + O + 1)

Also after the replacement of 2 pears by peaches the avg cost per fruit:
(248 - 2x + 2y)/(A + O) = 16
(248 -2(3(A + O + 1)))/(A + O) = 16
(248 - 6 - 6(A + O))/(A + O) = 16
242/(A + O) = 16 + 6
Therefore, A + O = 242/22 = 11

i.e Number of fruits initially in the basket = 11.

Avg cost after an pear is replaced by peach:
(248 - x + y)/(A + O) = (248 - 36)/11 = 212/11 = 19.27....

Simultaneous Equation Question - 1

Question:
A basket containing a certain number of pears and peaches costs Rs. 248. If 1 pear is added to the basket, the average cost per fruit in the basket increases by Rs. 2 and if 1 peach is added to the basket, the average cost per fruit in the basket decreases by Rs. 1. It is also known that if 2 pears are replaced with 2 peaches, the average cost per fruit in the basket becomes Rs. 16.Find the total number of fruits in the basket initially, and the the average cost per fruit in the basket after an pear is replaced by an peach.

SOLUTION