Previous Year Questions

Let the amount loaned to Z be Rs. P.

At the end of his terms, Z would pay = P(1 + r/100)³

So, amount loaned to X = Rs. 3P/5

At the end of his terms, X would pay = (3P/5)(1 + 3r/100)²

From I alone:

P(1 + r/100)³ : (3P/5)(1 + 3r/100)² = 3087:2116

[(100 + r)/100]³ : (3/5)[(100 + 3r)/100]² = 3087:2116

(100 + r)³ : (100 + 3r)² = (60 * 3087):2116

529(100 + r)³ = (15 * 3087)(100 + 3r)² .. (i)

So, we can find the value of r. But we can't determine the value of P. So, we cannot find the amounts/interests they paid. So, I alone is not sufficient.

From II alone:

If X took Rs. P as loan, then amount paid = P(1 + 3r/100)² - P

P(1 + 3r/100)² - P = 2580

P(10000 + 9r² + 600r) - 10000P = 25800000

P(9r² + 600r) = 25800000 .. (ii)

We cannot determine P or r. So, II alone is not sufficient.

From I and II together:

We derived equations (i) and (ii) from each statement (statement I and statement II).

529(100 + r)³ = (15 * 3087)(100 + 3r)² .. (i)

From equation (i) r=5 i.e., rate of interest = 5%

Substitute r=5 in equation (ii)

P(9r² + 600r) = 25800000 .. (ii)

P = 8000

At the end of his terms, Z would pay = P(1 + r/100)³ = 9261

At the end of his terms, X would pay = (3P/5)(1 + 3r/100)² = 6348

Hence the required difference = 2913

So, both the statements together are necessary.