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- Question
- If the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, then the resulting fraction is equal to the 1/2. If how ever the numerator is increased by 1, then denominator is decreased by 2, then the resulting fraction is equal to 3/5. Find the original fraction?
Options- A. 2/7
- B. 3/5
- C. 1/7
- D. 2/5
- Correct Answer
- 2/7
ExplanationLet the fraction be x / y.
According to the question,
( x+2)/(y+1) = 1/2
? 2x + 4 = y+1
? 2x - y = -3 .........................(i)
Again according to the question,
(x+1)/(y-2) = 3/5
? 5x +5 = 3y - 6
? 5x - 3y = -11..........................(ii)
on multiplying Eq. (i) by 3 and then subtracting from Eq. (ii) we get,
multiplying Eq. (i) by 3
6x - 3y = -9
subtracting from Eq. (ii)
5x- 3y - ( 6x - 3y ) = -11 - (-9)
5x- 3y - 6x + 3y = -11 + 9
- x = - 2
x= 2
On putting the value of x in Eq. (i) we get
2x- y = -3
2 x 2 - y = -3
? 2 x 2 -y = -3
? -y = -3 - 4
? y = 7
? Original fraction = x/y =2/7 - 1. The simplified form of log(75/16) -2 log(5/9) +log(32/343) is?
Options- A. log 2
- B. 2 log 2
- C. log 3
- D. log 5 Discuss
- 2. If log 2 = 0.3010 then log 5 equals to?
Options- A. 0.3010
- B. 0.6990
- C. 0.7525
- D. Given log 2, it is not possible to calculate log 5 Discuss
- 3. If log 102 =0.3010 and log 107 = 0.8451, then the value of log 10 2.8 is?
Options- A. 0.4471
- B. 1.4471
- C. 2.4471
- D. 14.471 Discuss
- 4. A merchant has announced 25% rebate on prices of ready made garments at the time of sale. If a purchaser needs to have a rebate of ? 400, then how many shirts, each costing ? 320, should he purchase?
Options- A. 10
- B. 7
- C. 6
- D. 5 Discuss
- 5. In the year 2011, Shantanu gets a total of 3832.5 Rupee as his pocket allowence. Find his pocket allowence per day.
Options- A. 9.5 Rupees
- B. 10.5 Rupees
- C. 12.5 Rupees
- D. 11.5 Rupees Discuss
- 6. 26.003 - 154 .001 ÷ 6.995 =?
Options- A. 4
- B. 18
- C. 9
- D. 10 Discuss
- 7. Given that log 10 2 = 0.3010, then log 2 10 is equal to?
Options- A. 0.3010
- B. 0.6990
- C. 1000 / 301
- D. 699 / 301 Discuss
- 8. The sum of 4 consecutive even number is 284. What would be the smallest number?
Options- A. 72
- B. 74
- C. 68
- D. 66 Discuss
- 9. A man travels 35 km partly at 4 km/hr and at 5 km/hr. If he covers former distance at 5 km/hr and later distance at 4 km/hr, he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is
Options- A. 9 hours
- B. 7 hours
- C. 4.5 hours
- D. 8 hours Discuss
- 10. The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
Options- A. Rs. 960
- B. Rs. 840
- C. Rs. 1020
- D. Rs. 760 Discuss
More questions
Correct Answer: log 2
Explanation:
Given Exp. = log75/16 - 2 log5/9 + log32/343
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2
Correct Answer: 0.6990
Explanation:
log 5 = log 10 /2 = log 10 - log 2
= 1 - 0.3010 = 0.6990
Correct Answer: 0.4471
Explanation:
log102.8 = log10(28/10)
= log 28 - log 10
= log (7 x 4 ) - log 10
= log 7 + 2 log 2 - log 10
= 0.8451 + 2 x 0.3010 - 1
= 0.8451 + 0.6020 - 1
= 0.4471
Correct Answer: 5
Explanation:
? Marked price of a shirt = ? 320
Discount on a shirt = 320 x 25/100 = ? 80
? Number of shirts has to be purchased to get a rebate of ? 400 = 400/80 = 5
Correct Answer: 10.5 Rupees
Explanation:
Allowance per day = total allowance / number of days in year
= 3832.5 / 365
= 10.5 Rupees
Correct Answer: 4
Explanation:
? = 26.003 - 154.001 ÷ 6.995
= 26 - 154 ÷ 7 = 26 - 22 = 4
Correct Answer: 1000 / 301
Explanation:
log2 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010
= 1000 / 301
Correct Answer: 68
Explanation:
Let four consecutive even numbers are x, x+2, x+4, x+6.
According to the question
? x + x+2 + x+4 + x+6 = 284
? 4x + 12 = 284
? 4x = 272
? x = 272 / 4 = 68
Correct Answer: 8 hours
Explanation:
Suppose the man covers first distance in x hrs. and second distance in y hrs.
Then , 4x + 5y = 35 and 5x +4y= 37
Solving these equation , we get
X=5 and y=3
Total time taken = (5+3) hrs= 8hrs
Correct Answer: Rs. 1020
Explanation:
| T.D. = | ❨ | B.G. x 100 | ❩ | = Rs. | ❨ | 270 x 100 | ❩ | = Rs. 750. |
| R x T | 12 x 3 |
∴ B.D. = Rs.(750 + 270) = Rs. 1020.
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