CAT (QA) PYQs

Gopal borrows Rs. $X$ from Ankit at $8 \%$ annual interest. He then adds Rs. $Y$ of his own money and lends Rs. $X+Y$ to Ishan at $10 \%$ annual interest. At the end of the year, after returning Ankit's dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. $X+2Y$ to Ishan at $10 \%$, then the net interest retained by him would have increased by Rs. $150$. If all interests are compounded annually, then find the value of $X+Y$.

A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by Rs. $1125$. Then the principal amount in rupees is