Interest - Study Mode

[#21] A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs. 5100 more. The sum is
Correct Answer

(D) Rs. 1, 70, 000

Explanation

Solution: $$eqalign{
& { ext{Let the sum be Rs}}{ ext{. }}x{ ext{ and}} cr
& { ext{original rate be R}}\% cr
& { ext{Then,}} cr
& Rightarrow frac{{x imes left( {{ ext{R}} + 1}
ight) imes 3}}{{100}} - frac{{x imes { ext{R}} imes 3}}{{100}} = 5100 cr
& Rightarrow 3{ ext{R}}x + 3x - 3{ ext{R}}x = 510000 cr
& Rightarrow 3x = 510000 cr
& Rightarrow x = 170000. cr
& { ext{Hence,}} cr
& { ext{Sum}} = { ext{Rs}}.170000 cr} $$

[#22] What equal installment of annual payment will discharge a debt which is due as Rs. 848 at the end of 4 years at 4% per annum simple interest ?
Correct Answer

(A) Rs. 200
(F) Rs. 200

Explanation

Solution: Let the annual installment be Rs. x. Then, $$ Rightarrow left[ {x + left( {frac{{x imes 3 imes 4}}{{100}}}
ight)}
ight] + $$ xa0 xa0 $$left[ {x + left( {frac{{x imes 2 imes 4}}{{100}}}
ight)}
ight] + $$ xa0 xa0 $$left[ {x + left( {frac{{x imes 1 imes 4}}{{100}}}
ight)}
ight] + $$ xa0 xa0 $$x = 848$$ $$eqalign{
& Leftrightarrow frac{{28x}}{{25}} + frac{{27x}}{{25}} + frac{{26x}}{{25}} + x = 848 cr
& Leftrightarrow 106x = 848 imes 25 cr
& Leftrightarrow 106x = 21200 cr
& Leftrightarrow x = 200 cr} $$ Short Cut Method : The annual payment that will discharge a debt of Rs. A due in t years at the rate of interest r % p.a. is. $$eqalign{
& frac{{100{ ext{A}}}}{{100t + frac{{rtleft( {t - 1}
ight)}}{2}}} cr
& herefore { ext{Annual installment}} cr
& = { ext{Rs}}{ ext{.}}left[ {frac{{100 imes 848}}{{100 imes 4 + frac{{4 imes 4 imes 3}}{2}}}}
ight] cr
& = { ext{Rs}}{ ext{.}}left( {frac{{100 imes 848}}{{424}}}
ight) cr
& = { ext{Rs}}{ ext{. }}200 cr} $$

[#23] A man buys a TV priced at Rs. 16000. He pays Rs. 4000 at once and the rest after 15 months on which he is charges a simple interest at the rate of 12% per year. The total amount he pays for TV is = ?
Correct Answer

(C) Rs. 17800

Explanation

Solution: Total price of TV = Rs. 16000 Initial payment = Rs. 4000 Remaining amount = Rs. 12000 Simple interest in 15 months for Rs. 12000 $$eqalign{
& Rightarrow { ext{S}}{ ext{.I}}{ ext{. = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} cr
& Rightarrow { ext{S}}{ ext{.I}}{ ext{. = }}frac{{12000 imes 12 imes 15}}{{100 imes 12}} cr
& Rightarrow { ext{S}}{ ext{.I}}{ ext{. = Rs}}{ ext{. 1800}} cr} $$ ⇒ With S.I. total amount to be paid for principal amount Rs. 12000 = Rs. (12000 + 1800) = Rs. 13800 = Therefore, total amount he pays for the TV is = 4000 + 13800 = Rs. 17800

[#24] If the ratio of principal and the simple interest of 5 years is 10 : 3, then the rate of interest is = ?
Correct Answer

(A) 6%

Explanation

Solution: $$eqalign{
& frac{{ ext{P}}}{{{ ext{S}}{ ext{.I}}{ ext{.}}}} = frac{{10}}{3} cr
& { ext{Let Principal = 10}} cr
& { ext{S}}{ ext{.I}}{ ext{. for 5 years = 3}} cr
& { ext{S}}{ ext{.I}}{ ext{. for 1 year = 0}}{ ext{.6}} cr
& { ext{Rate = }}frac{{{ ext{S}}{ ext{.I}}{ ext{.}}}}{{{ ext{Principal}}}} imes 100 cr
& { ext{Rate = }}frac{{0.6}}{{10}} imes 100 cr
& ,,,,,,,,,,,, = 6\% cr} $$

[#25] Mr. Dutta desired to deposit his retirement benefit of Rs. 3 lacs partly to a post office and partly to a bank at 10% and 6% simple interests respectively. If his monthly income was Rs. 2000, then the difference of his deposits in the post office and in the bank was = ?
Correct Answer

(D) Rs. Nil

Explanation

Solution: 10% of Rs. 3 Lacs = 30000 6% of Rs. 3 Lacs = 18000 1 month interest income = 2000 ∴ 1 year interest income = 2000 × 12 = 24000 Profit of Bank = 24000 - 18000 = 6000 Profit of Post Office = 30000 - 24000 = 6000 ∴ Ratio of profit = 6000 : 6000 = 1 : 1 So, amount deposited = Rs. 150000 each And difference = 0