Friday, June 14, 2013

XAT 2012 : Quant Question 66 : Mensuration Surface Area

Question

A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:

A.    1000 times
B.    100 times
C.    10 times
D.    No Change
E.    None of the above

Correct Answer : 10 times. Choice C

Explanatory Answer
Let the radius of the small spheres be ‘r’ cm.
The amount of metal remains the same in both cases.

Hence, volume of the spherical metal of radius 10 cm should be equal to the volume of the 1000 smaller spheres of radius ‘r’ cm put together.





Therefore, r = 1 cm.
Surface area of a spherical metal of radius 10 cm is
 


Surface area of 1000 smaller spheres put together is



Thus the surface area increased by 10 times.

Wednesday, May 15, 2013

XAT 2012 Quant Q65 : Siimple Interest

This question appeared in the XAT 2012 quant section. Question 65.

Question

A man borrows Rs. 6000 at 5% interest, on reducing balance, at the start of the year. If he repays Rs. 1200 at the end of each year, find the amount of loan outstanding, in Rupees, at the beginning of the third year.

A. 3162.75
B. 4125.00
C. 4155.00
D. 5100.00
E. 5355.00

Correct Answer : Choice C. Rs.4155.00

Explanatory Answer
Interest payable @ the end of the first year @ 5% interest on Rs 6000 =




Amount payable @ the end of the first year = Rs 6000 + Rs 300 = Rs 6300
Amount paid @ the end of the first year = Rs 1200
Therefore, Principal for the second year = Rs 6300 – Rs 1200 = Rs 5100

Interest payable @ the end of the second year @ 5% interest on Rs 5100 =




Amount payable @ the end of the second year = Rs 5100 + Rs 255 = Rs 5355
Amount paid @ the end of the second year = Rs 1200
Therefore, Principal for the third year = Rs 5355 – Rs 1200 = Rs 4155

Thus, the amount of loan outstanding at the beginning of the third year = Rs 4155.