Simple interest
- A man invests a certain sum of money at 6% per annum simple interest and another at 7% per annum simple interest. His income from interest after 2 yr was ₹ 792. Also, half of the first sum is equal to one-third of the second sum. The total sum invested was ?
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Let the sum be P and Q, respectively.
Then, (P x 6 x 2)/100 + (Q x 7 x 2)/100 = 792
⇒ 6P + 7Q = 39600 ...(i)
Also P/2 = Q/3 ⇒ 3P = 2Q ... (ii)Correct Option: C
Let the sum be P and Q, respectively.
Then, (P x 6 x 2)/100 + (Q x 7 x 2)/100 = 792
⇒ 6P + 7Q = 39600 ...(i)
Also P/2 = Q/3 ⇒ 3P = 2Q ... (ii)
On solving Eqs . (i) and (ii), we get P = 2400 and Q = 3600
∴ Total sum = (2400 + 3600) = ₹ 6000
- A man buys a music system valued at ₹ 8000. He pays ₹ 3500 at once and rest 18 months later, on which he is charged simple interest at the rate of 8% per annum . Find the total amount he pays for the music system ?
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Cost of the music system = ₹ 8000
Money paid at once = ₹ 3500
Money left = (8000 - 3500) = ₹ 4500
Time = (18/12) = 3/2 yr and R = 8% per annum
SI = PTR/100 = (4500 x 3/2 x 8)/100 = ₹ 540Correct Option: B
Cost of the music system = ₹ 8000
Money paid at once = ₹ 3500
Money left = (8000 - 3500) = ₹ 4500
Time = (18/12) = 3/2 yr and R = 8% per annum
SI = PTR/100 = (4500 x 3/2 x 8)/100 = ₹ 540
Money to be paid at the end = (4500 + 540) = ₹ 5040
∴ Cost of music system = (3500 + 5040) = ₹ 8540
- Out of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. It the simple interest for 2 yr from all these investments amounts to ₹ 600 , find the original sum.?
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Rest part = 1 - (1/3 + 1/6) = 1/2
Average rate per cent annum on the total sum
= [(1/3) x 3] + [(1/6) x 6] + [(1/2) x 8] = 6%Correct Option: A
Rest part = 1 - (1/3 + 1/6) = 1/2
Average rate per cent annum on the total sum
= [(1/3) x 3] + [(1/6) x 6] + [(1/2) x 8] = 6%
∴ P = (100 x SI)/(R x T) = (100 x 600)/(6 x 2) = ₹ 5000
- The annual payment of ₹ 160 in 5 yr at 5 % per annum simple interest will discharge a debt of
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Given, annual payment = ₹ 160
R = 5% T = 5 yr debt (p) = ?
According to the formula.
Annual payment = 100P / [100 x T + {RT (T - 1)/2}]Correct Option: B
Given, annual payment = ₹ 160
R = 5% T = 5 yr debt (p) = ?
According to the formula.
Annual payment = 100P / [100 x T + {RT (T - 1)/2}]
⇒160 = 100P / [5 x 100 + {(5 x 4 x 5)/2}]
⇒ 160 = 100P/550
∴ P = (550 x 160) / 100
= 55 x 16 = ₹ 880
- Pratap borrowed some money from Arun at simple interest. The rate of interest for the first 3 years was 12% for the next 5 years was 16% and beyond this it was 20%. If the simple interest for 11 years was more than the money borrowed by Rs. 6080. What was the money borrowed ?
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Let the sum be P.
SI = SI for first 3 years + SI for next 5 years + SI for next 3 years
⇒ P + 6080 = (P x 12 x 3) / 100 + (P x 16 x 5) / 100 + (P x 20 x 3) / 100Correct Option: C
Let the sum be P.
SI = SI for first 3 years + SI for next 5 years + SI for next 3 years
⇒ P + 6080 = (P x 12 x 3) / 100 + (P x 16 x 5) / 100 + (P x 20 x 3) / 100
⇒ P + 6080 = (36P + 80P + 60P) / 100
⇒ 100 x (P + 6080) = 176P
∴ P = 608000 / 76 = 8000
