Discussion
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- Question
- During the first year, the population of a village is increased by 5% and the second year, it is diminished by 5%. At the end of the second year, its population was 47880. What was the population at the beginning of the first year?
Options- A. 45500
- B. 48000
- C. 43500
- D. 53000
- Correct Answer
- 48000
ExplanationLet the population at the beginning of the first year be N .
Then, according to the question,
N x [1+ 5/100] x [1 - 5/100] = 47880
? N x (105/100) x (95/100) = 47880
? N = 47880 x (100/105) x (100/95) = 48000 - 1. The simple interest on a certain sum of money for 3 yr at 8 % pa is half the compound interest on ? 8000 for 2 yr at 10 % pa. Find the sum on which simple interest is calculated
Options- A. ? 3500
- B. ? 3800
- C. ? 4000
- D. ? 3600 Discuss
- 2. A sum of ? 8448 is to be divided between A and B who are respectively 18 and 19 yr old, in such a way that if their shares be invested at 6.25 % per annum at compound interest, they will receive equal amounts on attaining the age of 21 yr. The present share of A is
Options- A. ? 4225
- B. ? 4352
- C. ? 4096
- D. ? 4000 Discuss
- 3. A sum of ? 11000 was taken as loan. This is to be paid in two equal annual installments. If the rate of interest be 20% compounded annually, then the value of each installment is
Options- A. ? 7500
- B. ? 7000
- C. ? 7100
- D. ? 7200 Discuss
- 4. An amount is invested in a bank at compound rate of interest . The total amount, including interest, after first and third year is ? 1200 and ? 1587, respectively . What is the rate of interest?
Options- A. 10 %
- B. 3.9 %
- C. 12 %
- D. 15 % Discuss
- 5. A man borrows ? 5100 to be paid back with compound interest at the rate of 4 % pa by the end of 2 yr in two equal yearly installments. How much will each installment be?
Options- A. ? 2704
- B. ? 2800
- C. ? 3000
- D. ? 2500 Discuss
- 6. What amount will be received on a sum of ? 1750 in 2 1/ 2 yr, if the interest is compounded at the rate of 8% pa?
Options- A. ? 2125
- B. ? 2122.85
- C. ? 2100
- D. ? 2200 Discuss
- 7. Find what is that first years in which a sum of money will become more than double in amount if put out at compound interest at the rate of 10% per annum?
Options- A. 6th years
- B. 7th years
- C. 8th years
- D. Data inadequate Discuss
- 8. If P = { 1, 2, 3 } and Q = { 4 , 5 } then what is the value of P × Q?
Options- A. { (4 , 5) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
- B. { (1 , 4) , (4 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
- C. { (1 , 4) , (1 , 5) , (2 , 4) , (3 , 5) , (3 , 4) , (3 , 5) }
- D. { (1 , 4) , (1 , 5) , (2 , 4) , (2 , 5) , (2 , 4) , (3 , 5) } Discuss
- 9. If A and B have n elements in common, how many elements do A × B and B × A have in common?
Options- A. n
- B. n3
- C. n2
- D. None of these Discuss
- 10. If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ? B) ? (A ? C).
Options- A. {c}
- B. {a}
- C. {b}
- D. {d} Discuss
Compound Interest problems
Search Results
Correct Answer: ? 3500
Explanation:
CI = 8000 x (1 + 10/100)2 - 8000
= 8000 x (11/10) x (11/10) - 8000
= ? 9680 - 8000
= ? 1680
? Sum = (840 x 100)/(3 x 8) = ? 3500
[ ? SI is half of CI ]
? SI = 1680/2 = ? 840
Correct Answer: ? 4096
Explanation:
Let shares of A and B be ? N and ? (8448 - N), respectively,
Amount got by A after 3 yr = Amount got by B after 2 yr
N(1 + 6.25/100)3 = (8448 - N) x (1 + 6.25/100)2
? 1 + 6.25/100 = (8448 - N)/N
? 1 + 1/16 = (8448 - N)/N
? 17/16 = (8448 - N)/N
? 17N = 135168 - 16N
? N = 4096
Correct Answer: ? 7200
Explanation:
Let value of each installment be ? N .
Then, N/(1 + 20/100) + N/(1 + 20/100)2 = 11000
? N(5/6 + 25/36) = 11000
? N(56/36) = 11000
? N = ? 7200
Correct Answer: 15 %
Explanation:
Let amount be ? P and rate of interest be R % annually .
According to the question,
Amount after 1st yr = ? 1200
? P(1 + R/100) = 1200 ...(i)
Amount after 3rd yr = 1587
? P(1 + R/100)3 = 1587 ...(ii)
On dividing Eq. (ii) from Eq. (i), we get
(1 + R/100)2 = 1587/1200 = 529/400
? 1 + R/100 = 23/20
? R/100 = 3/20
? R = 15 %
Correct Answer: ? 2704
Explanation:
Let each installment be ? N .
Then , according to the question ,
N/(1 + 4/100 ) + N/(1 + 4/100 )2 = 5100
? 25N/26 + 625N/676 = 5100
? 1275N = 5100 x 676
? N = (5100 x 676)/1275 = ? 2704
Correct Answer: ? 2122.85
Explanation:
Given, P = ? 1750, R = 8%,
n = 2 and a/b = 1/2
According to the formula,
Amount = P(1 + R/100)n x [1 + {(a/b) x R}/100]
=1750 (1 + 8/100 )2 [1 + {(1/2) x 8} /100]
=1750 (27/25)2 x 26/25
= 1750 x (27/25) x (27/25) x (26/25)
=? 2122.848
= ? 2122.85
Correct Answer: 8th years
Explanation:
Here, P(1 + 10/100)t > 2P
? (11/10)t > 2
When t = 8 ? (11/10)8 = 2.14358
t =7 ? (11/10)7 = 1.9487
By trial, [11 x 11 x 11 x 11 x 11 x 11 x 11 x 11] / [10 x 10 x 10 x 10 x 10 x 10 x 10 x 10] >2
Hence, the first years in which sum of money will become more than double in amount is 8th year
Correct Answer:
Explanation:
The Cartesian product X × Y of sets X , Y is the set of all ordered pairs ( x , y ).
Two ordered pairs ( x1 , y1 ), ( x2 , y2 ) .
Given that P = { 1, 2, 3 } and Q = { 4 , 5 } then,
P x Q = { 1, 2, 3 } x { 4 , 5 }
? P x Q = { 1 } x { 4 , 5 } , { 2 } x { 4 , 5 } , { 3 } x { 4 , 5 }
? P x Q = { 1 , 4 } , { 1 , 5 } , { 2 , 4 } , { 2 , 5 } , { 3 , 4 }, { 3 , 5 }
? P x Q = { (1 , 4 ) , ( 1 , 5 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 3 , 4 ), ( 3 , 5) }
Correct Answer: n2
Explanation:
NA
Correct Answer: {c}
Explanation:
A ? B = {a, b, c} ? {c, d, e, f}
A ? B = { c }
A ? C = { a, b, c } ? { c, d, e }
A ? C = { c }
? (A ? B) ? (A ? C) = { c }.
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