A merchant lent out Rs. 20000 in two parts, one at 8% and other at 10% interest. The yearly average comes out to be 9.2%.
Which of the following are correct?
(A) Amount lent at 10% is Rs. 12000.
(B) Amount lent at 8% is Rs. 12000.
(C) Amount lent at 10% is Rs. 8000.
(D) Amount lent at 8% is Rs. 8000.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (D) only
Let Rs. x be lent at 8%; then Rs. (20000 − x) is lent at 10%. The total yearly interest equals 9.2% of the whole sum:
\( \displaystyle 0.08x+0.10(20000-x)=0.092\times 20000 \)
\( \displaystyle 0.08x+2000-0.10x=1840 \)
\( \displaystyle 0.02x=160 \)
\( \displaystyle x=8000 \)
So Rs. 8000 is lent at 8% and Rs. 20000 − 8000 = Rs. 12000 at 10%.
Checking the statements
(A) Amount lent at 10% is Rs. 12000. — Correct. Rs. 12000 is lent at 10%.
(B) Amount lent at 8% is Rs. 12000. — Incorrect. Rs. 8000 is lent at 8%.
(C) Amount lent at 10% is Rs. 8000. — Incorrect. Rs. 12000 is lent at 10%.
(D) Amount lent at 8% is Rs. 8000. — Correct. Rs. 8000 is lent at 8%.
Shortcut: By the rule of alligation, amount at 8% : amount at 10% = (10 − 9.2) : (9.2 − 8) = 0.8 : 1.2 = 2 : 3. So the parts are \( \frac{2}{5}\times 20000=8000 \) at 8% and 12000 at 10%.