Interest - Study Mode

[#61] Tushar borrowed a sum of Rs. 12000 at 15% per annum from a money - lender on 13 th January, 1987 and return the amount on 8 th June, 1987 to clear his debt. Then the amount paid by Tushar to the money - lender to clear his debt was = ?
Correct Answer

(C) Rs. 12720

Explanation

Solution: Time = 18 + 28 + 31 + 30 + 31 + 8 = 146 days $$eqalign{
& { ext{Simple Interest}} cr
& { ext{ = }}frac{{12000 imes 15 imes 146}}{{365 imes 100}} cr
& { ext{ = Rs}}{ ext{. 720}} cr
& herefore { ext{Amount will be }} cr
& { ext{ = Rs}}{ ext{.}}left( {12000 + 720}
ight){ ext{ }} cr
& { ext{ = Rs}}{ ext{. 12720}} cr} $$

[#62] Vishwas borrowed a total amount of Rs. 30000, part of it on simple interest rate of 12 p.c.p.a. and remaining on simple interest rate of 10 p.c.p.a. If at the end of 2 year she paid in all Rs. 36480 to settle the loan amount, what was the amount borrowed at 12 p.c.p.a ?
Correct Answer

(A) Rs. 12000

Explanation

Solution: Let the sum borrowed at 12% p.a. be Rs. x and that borrowed at 10% p.a. be Rs. (30000 - x) S.I. at the end of 2 years = Rs. (36480 - 30000) = Rs. 6480 $$ herefore left( {frac{{x imes 12 imes 2}}{{100}}}
ight) + $$ xa0xa0 $$left[ {frac{{left( {30000 - x}
ight) imes 10 imes 2}}{{100}}}
ight]$$ xa0 xa0 $$ = 6480$$ $$eqalign{
& Leftrightarrow 24x + 600000 - 20x = 648000 cr
& Leftrightarrow 4x = 48000 cr
& Leftrightarrow x = 12000 cr} $$

[#63] A sum of Rs. 18750 is left by a will by a father to be divided between the two sons, 12 and 14 years of age, so that when they attain maturity at 18, the amount (principal + interest) received by each at 5 percent simple interest will be the same. Find the sum alloted at present to each son.
Correct Answer

(C) Rs. 9000, Rs. 9750

Explanation

Solution: Let the two sums be Rs. x and Rs. (18750 - x). Then, $$ = x + frac{{x imes 5 imes 6}}{{100}} = left( {{ ext{18750}} - x}
ight) + $$ xa0 xa0 xa0 $$frac{{left( {{ ext{18750}} - x}
ight) imes 5 imes 4}}{{100}}$$ $$eqalign{
& Leftrightarrow x + frac{{30x}}{{100}} = left( {{ ext{18750}} - x}
ight) + 3750 - frac{{20x}}{{100}} cr
& Leftrightarrow 2x + frac{x}{2} = 22500 cr
& Leftrightarrow frac{{5x}}{2} = 22500 cr
& Leftrightarrow x = left( {frac{{22500 imes 2}}{5}}
ight) cr
& Leftrightarrow x = 9000 cr} $$ So the other sum will be = ( 18750 - 9000) = 9750 Hence, The two sums are Rs. 9000, Rs. 9750

[#64] I had Rs. 10000 with me. Out of this money I lent some money to A for 2 years @ 15% simple interest. I lent the remaining money to B for an equal number of years @18% simple interest. After 2 years, I found that A had given me Rs. 360 more as interest as compared to B. The amount of money which I had lent to B must have been.
Correct Answer

(C) Rs. 4000

Explanation

Solution: Let the sum lent to A be Rs. x. and that lent to B be Rs. (10000 - x) Then, $$eqalign{
& Rightarrow frac{{x imes 15 imes 2}}{{100}} - frac{{left( {10000 - x}
ight) imes 18 imes 12}}{{100}} = 360 cr
& Rightarrow 30x - 360000 + 36x = 36000 cr
& Rightarrow 66x = 396000 cr
& Rightarrow x = 6000 cr} $$ Hence, Sum lent to B = Rs. (10000 - 6000) = Rs. 4000

[#65] A certain sum of money amount to Rs 2200 at 5% interest Rs 2320 at 8% interest in the same period of time. The period of time is = ?
Correct Answer

(A) 2 years

Explanation

Solution: $$eqalign{
& { ext{P}} + { ext{SI = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} + { ext{P}} cr
& Rightarrow 2200{ ext{ = }}frac{{{ ext{P}} imes 5 imes { ext{T}}}}{{100}} + { ext{P}} cr} $$ ⇒ 2200 × 100 = 5PT + 100P ......... (i) $$ Rightarrow 2320 = frac{{{ ext{P}} imes 8 imes { ext{T}}}}{{100}} + { ext{P}}$$ ⇒ 2320 × 100 = 8PT + 100P ⇒ 2320 × 100 = 3PT + 5PT + 100P ............(ii) Value of equation (i) put equation (ii) ⇒ 2320 × 100 = 3PT + 2200 × 100 ⇒ 3PT = 120 × 100 ⇒ PT = 4000 Value of PT in equation (i) ⇒ 2200 × 100 = 5 × 4000 + 100P ⇒ 220000 - 20000 = 100P $$eqalign{
& Rightarrow { ext{P = }}frac{{200000}}{{100}} cr
& Rightarrow { ext{P = Rs 2000}} cr
& { ext{Using this formula}} cr
& left( {x08ecause { ext{SI = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}}}
ight) cr
& herefore { ext{200}} = frac{{2000 imes 5 imes { ext{T}}}}{{100}} cr
& Rightarrow { ext{T}} = frac{{200}}{{100}}{ ext{ = 2 years}} cr
& cr
& { ext{ }}{x08f{Alternate:}} cr
& left( {8 - 5}
ight)\% = 2320 - 2200 cr
& Rightarrow 3\% = 120 cr
& Rightarrow 1\% = 40 cr
& Rightarrow 5\% = 200 cr
& { ext{Principal = 2200 - 200}} cr
& ,,,,,,,,,,,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 2000}} cr
& { ext{SI = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} cr
& Rightarrow { ext{200}} = frac{{2000 imes 5 imes { ext{T}}}}{{100}} cr
& Rightarrow { ext{T}} = frac{{200}}{{100}}{ ext{ = 2 years}} cr} $$