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- Question
- There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the first number and twice the second number is 120. Which is the larger number?
Options- A. 32
- B. 12
- C. 14
- D. 35
- Correct Answer
- 32
ExplanationLet us assume the first number is x and second number is y.
According to question,
sum of twice the first number and thrice the second number is 100.
2x + 3y = 100 ...................(1)
and sum of thrice the first number and twice the second number is 120.
3x + 2y = 120...................(2)
Subtract equation (1) from Equation (2) after multiply 2 with Equation (1) and 3 with Equation (2), we will get.
3(3x + 2y) - 2(2x + 3y) = 3 x 120 - 2 x 100
9x + 6y - 4x - 6y = 360 - 200
5x = 160
x = 32
put the value of x in equation (1)
2 x 32 +3y = 100
3y = 100 - 64
3y = 36
y = 12
The larger Number is 32 . - 1. 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?
Options- A. ? 400
- B. ? 560
- C. ? 460
- D. ? 200 Discuss
- 2. 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?
Options- A. ? 9260
- B. ? 8540
- C. ? 8720
- D. ? 9410 Discuss
- 3. 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?
Options- A. ? 5800
- B. ?. 6200
- C. ? 6000
- D. ? 5900 Discuss
- 4. A borrowed ? 4800 from B at 9% per annum simple interest for 3 yr. He, then added some more money to the borrowed sum and lent it to C for the same period at 12% per annum simple interest. If A gains ? 720 in the whole transaction, how much money did he add from his side?
Options- A. ? 500
- B. ? 740
- C. ? 640
- D. ? 800 Discuss
- 5. A person closer his account in an investment scheme by withdrawing ? 10000. One year ago, he had withdraw ? 6000. Two years ago, he had withdrawn ? 5000. Three years ago, he had not withdrawn any money. How much money had he deposited approximately at the time of opening the account 4 yr ago, if the annual simple interest is 10%?
Options- A. ? 15600
- B. ? 16500
- C. ? 17280
- D. None of these Discuss
- 6. Mr. Pawan invests an amount of ? 242000 at the rate of 4% per annum for 6 yr to obtain a simple interest, later he invests the principal amount as well as the amount obtained as simple interest for another 4 yr at the same rate of interest. What amount of simple interest will be obtained at the end of the last 4 yr?
Options- A. ? 4800
- B. ? 4850.32
- C. ? 4801.28
- D. ? 4700 Discuss
- 7. Rajnish invested certain sum in three different schemes P, Q and R with the rates of interest 10% per annum, 12% per annum and 15% per annum, respectively. If the total interest accrued in 1 yr was ? 3200 and the amount invested in scheme R was 150% of the amount invested in scheme Q. what was the amount invested in scheme Q?
Options- A. ? 8000
- B. ? 9000
- C. ? 5000
- D. ? 3050 Discuss
- 8. The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs. 1.50. The sum is?
Options- A. Rs. 600
- B. Rs. 500
- C. Rs. 400
- D. Rs. 300 Discuss
- 9. If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest is?
Options- A. Rs. 150
- B. Rs. 152.50
- C. Rs. 160
- D. Rs. 162.50 Discuss
- 10. A sum amounts to Rs. 1352 in 2 years at 4% compound interest.The sum is?
Options- A. Rs. 1300
- B. Rs. 1250
- C. Rs. 1260
- D. Rs. 1200 Discuss
More questions
Correct Answer: ? 560
Explanation:
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
Correct Answer: ? 8540
Explanation:
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
Correct Answer: ? 6000
Explanation:
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
Correct Answer: ? 800
Explanation:
Let the money added be ? P, Then,
[(4800 + P) x 12 x 3]/100 - (4800 x 9 x 3)/100 = 720
? (4800 + P) x 36 - (4800 x 27) = 720 x 100
? (4800 + P) x 4 - (4800 x 3) = 8000
? 4800 + P - (1200 x 3 ) = 2000
? P + 1200 = 2000
? P = 800
So, money added is ? 800.
Correct Answer: None of these
Explanation:
Suppose the person had deposited ? P at the time of opening the account .
? After one year he had P + (P x 10 x 1)/100 = ? 11P/10
After two years, he had
11P/10 + (11P/10 x 10 x 1)/100 = ? 121P/100 ...(i)
After withdrawn ? 5000 from ? 121P/100, the balance
= ? (121P - 500000)/100
After 3 yr, he had
(121P - 500000)/100 + [(121P - 500000)/100 x 10 x 1]/100
= 11(121P - 500000)/100 ... (ii)
After withdrawn ? 6000 from amount (ii) the balance
= (1331P/1000 - 11500)
? After 4 yr, he had ? (1331P - 5500000)/1000 + 10% of ? (1331P - 5500000)/1000
= ? (11/10) x (1331P/1000 - 11500) ... (iii)
After withdrawn ? 10000 from amount (iii) the balance =0
? 11/10(1331P/1000 - 11500) - 10000 = 0
? P = ? 15470
Correct Answer: ? 4801.28
Explanation:
In the case I,
SI = (P x R x T) /100 = (24200 x 4 x 6) / 100 = ? 5808
? Amount = Principal + SI
SI = 24200 + 5808 = 30008
In the case II,
SI = (30008 x 4 x 4) / 100 = ? 4801.28
Correct Answer: ? 5000
Explanation:
Let a, b and c be the amount invested in schemes P, Q and R, respectively.
Then, according to the question,
[(a x 10 x 1)/100] + [(b x 12 x 1)/100] + [(c x 15 x 1)/100] = 3200
? 10a + 12b + 15x = 320000 .....(i)
Now, c = 240% of b = 12b/5 ....(ii)
and c = 150% of a = 3a/2
? a = 2c/3 = (2/3 x 12/5) b = 8b/5 .....(iii)
From Eqs. (i), (ii) and (iii), we get
16b + 12b + 36b = 320000
? 64b = 320000
? b = 5000
? Sum invested in scheme Q = ? 5000
Correct Answer: Rs. 600
Explanation:
Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4
? Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
? 0.25 : 150 : : 100 : P
? P = (1.50 x 100) / 0.25 = Rs. 600
Correct Answer: Rs. 160
Explanation:
Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
? p x (112.5/100) x (112.5/100) - p = 170
? P [ 12656.25 - 10000 ] = 170 x 10000
? p = (170 x 10000) / 2656.25
Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160
Correct Answer: Rs. 1250
Explanation:
Let the sum be P.
Then, 1352 = P(1 +4/100)2
? 1352 = P x 26/25 x 26/25
? P = (1352 x 25 x 25) / (26 x 26) = 1250
? Principal = Rs. 1250
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