Simple interest
- Equal sum of money are lent to X and Y at 7.5% per annum for a period of 4 years and 5 years respectively. If the difference in interest, paid by them was ₹150, the sum lent to each was
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Let the sum lent be p.
∴ p × 7.5 × 5 - p × 7.5 × 4 = 150 100 100 ⇒ p × 7.5 × 1 = 150 100 ⇒ p = 150 × 100 = ₹ 2000 7.5
Second method to solve this question :
Here, P1 = P, R1 = 7.5%,
T1 = 4 years. , P2 = P, R2 = 7.5% , T2 = 5 years , S.I. = Rs. 150SI = P2T2 × R2 - P1T1 × R1 100
Correct Option: C
Let the sum lent be p.
∴ p × 7.5 × 5 - p × 7.5 × 4 = 150 100 100 ⇒ p × 7.5 × 1 = 150 100 ⇒ p = 150 × 100 = ₹ 2000 7.5
Second method to solve this question :
Here, P1 = P, R1 = 7.5%,
T1 = 4 years. , P2 = P, R2 = 7.5% , T2 = 5 years , S.I. = Rs. 150SI = P2T2 × R2 - P1T1 × R1 100 150 = P × 7.5 × 5 - P × 7.5 × 4 100
15000 = 7.5PP = 150000 75
P = ₹ 2000
- A sum of ₹1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part (In rupees) is
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Let first part be p and second part be(1750 – p )
According to the question,p × 8 = (1750 - p) × 6 100 100
⇒ 8p + 6p = 1750 × 6
⇒ 14p = 1750 × 6⇒ p = 1750 × 6 = ₹750 14
∴ Simple Interest = 8% of 750
Correct Option: A
Let first part be p and second part be(1750 – p )
According to the question,p × 8 = (1750 - p) × 6 100 100
⇒ 8p + 6p = 1750 × 6
⇒ 14p = 1750 × 6⇒ p = 1750 × 6 = ₹750 14
∴ Simple Interest = 8% of 750Simple Interest = 750 × 8 = ₹ 60 100
- A borrows ₹800 at the rate of 12% per annum simple interest and B borrows ₹910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal ?
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Let the period of time be T years.
From question , we have∴ 800 + 800 × 12 × T = 910 + 910 × 10 × T 100 100
⇒ 800 + 96 T = 910 + 91T
⇒ 96 T – 91 T = 910 – 800
⇒ 5T = 110
Correct Option: C
Let the period of time be T years.
From question , we have∴ 800 + 800 × 12 × T = 910 + 910 × 10 × T 100 100
⇒ 800 + 96 T = 910 + 91T
⇒ 96 T – 91 T = 910 – 800
⇒ 5T = 110⇒ T = 110 = 22 Years. 5
- The difference between the simple interest received from two different banks on ₹500 for 2 years is ₹2.50. The difference between their (per annum) rate of interest is :
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Here , The difference between the simple interest = ₹2.50
From the question ,500 × 2 × R1 - 500 × 2 × R2 = 2.5 100 100
where R1 & R2 are rate% of both banks
⇒ 10 (R1 – R2) = 2.5
⇒ R1 – R2 = 2.5 ÷ 10 = 0.25 % per annum
Second method to solve this question :
Here, P = Rs. 500 , y = Rs. 2.50, Difference in time = 2 years , Difference in rate = ?
Correct Option: B
Here , The difference between the simple interest = ₹2.50
From the question ,500 × 2 × R1 - 500 × 2 × R2 = 2.5 100 100
where R1 & R2 are rate% of both banks
⇒ 10 (R1 – R2) = 2.5
⇒ R1 – R2 = 2.5 ÷ 10 = 0.25 % per annum
Second method to solve this question :
Here, P = Rs. 500 , y = Rs. 2.50, Difference in time = 2 years , Difference in rate = ?500 = 2.50 × 100 (diff in rate) × 2
Different in rate = 0.25%
- A sum ₹ 1440 is lent out in three parts in such a way that the interest on first part at 2% for 3 yr, second part at 3% for 4 yr and third part at 4% for 5 yr equal . Then, the difference between the largest and the smallest sum is ?
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Let the first part be ₹ A.
second part be ₹ B
and third part be Rs C
According to the question.
(A x 2 x 3)/100 = (B x 3 x 4)/100 = (C x 4 x 5)/ 100Correct Option: B
Let the first part be ₹ A.
second part be ₹ B
and third part be Rs C
According to the question.
(A x 2 x 3)/100 = (B x 3 x 4)/100 = (C x 4 x 5)/ 100
⇒ 3A = 6B = 10C = k
∴ A = k/3, B = k/100 and C = k /10
Now, A + B + C = 1440
⇒ k/3 + k/6 + k/10 = 1440 ⇒ k = 2400
∴ so the difference = k/3 - k/10 = 7k/30 = 7/30 x 2400 = ₹ 560
