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- Question
- A man arranges to pay off a debt of ?3600 in 40 annual installments which form an Arithmetic Progression (A.P). When 30 of the installments are paid, he dies leaving one-third of the debt unpaid . Find the value of the first installment.
Options- A. 55
- B. 53
- C. 51
- D. 49
- Correct Answer
- 51
ExplanationLet us assume the first installment is a and difference between two consecutive installments is d.
According to question,
Sum of 40 Installments = 3600
Apply the formula Sum of first n terms in an Arithmetic Progression = Sn = n/2[ 2a + (n?1)d ]
where a = the first term, d = common difference, n = number of terms.
n/2[ 2a + (n?1)d ] = 3600
Put the value of a, n and d from question,
40/2[ 2a + (40 ?1)d ] = 3600
20[ 2a + 39d ] = 3600
[ 2a + 39d ] = 3600/20 = 180
2a + 39d = 180...........................(1)
Again according to given question,
After paying the 30 installments the unpaid amount = 1/3(total unpaid amount) = 3600 x 1/3
After paying the 30 installments the unpaid amount = 1200
So After paying the 30 installments the paid amount = 3600 - 1200 = 2400
Sum of 30 installments = 2400
30/2[ 2a + (30 ?1)d ] = 2400
[ 2a + (30 ?1)d ] = 2400 x 2/30
2a + 29d = 80 x 2 = 160
2a + 29d = 160..........................(2)
Subtract the Eq. (2) from Eq. (1), we will get
2a + 39d - 2a - 29d = 180 - 160
10d = 20
d = 2
Put the value of d in Equation (1), we will get
2a + 39 x 2 = 180
2a = 180 - 78
a = 102/2
a = 51
The value of first installment = a = 51 - 1. If the HCF of m and n is 1, then what are the HCF of m + n, m and HCF of m - n, n, respectively (where, m > n)?
Options- A. 2 and 1
- B. 1 and 1
- C. 1 and 2
- D. Cannot be determined Discuss
- 2. The sum of the digits of two-digit number is 14 and the difference between the two digits number is 2. What is the product of the two digits of the two-digit number?
Options- A. 56
- B. 48
- C. 45
- D. None of the above Discuss
- 3. The population of a town increase 4% annually but is decreases by emigration annually to the extent of 1/2%. What will be the increase percent in three years?
Options- A. 9.8
- B. 10
- C. 10.5
- D. 10.8 Discuss
- 4. If 2log 4x = 1 + log 4 (x-1), find the value of x.?
Options- A. 2
- B. 1
- C. 4
- D. 3 Discuss
- 5. A persom invests ? 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs, he has to withdraw the entire money after 3 yr for which the bank allowed him a lower rate of interest. If he gets ? 3320 less than, what he would have got at the end of 5 yr the rate of interest allowed by bank is
Options- A. 78/9%
- B. 87/9%
- C. 78/9%
- D. 77/9% Discuss
- 6. If log 90 = 1.9542 then log 3 equals to?
Options- A. 0.9771
- B. 0.6514
- C. 0.4771
- D. 0.3181 Discuss
- 7. What is the probability that a leap year selected randomly will have 53 Mondays?
Options- A. 2/7
- B. 5/7
- C. 1/7
- D. Data inadequate Discuss
- 8. Two poles of ht. a and b meters are p meters apart ( b > a). The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is :
Options- A. a+b ab
- B. p a+b
- C. ab a+b
- D. a+b p Discuss
- 9. Of all the chords of a circle passing through a given point in it, the smallest is that which :
Options- A. Is trisected at the point
- B. Is bisected at the point
- C. Passes through the centre
- D. None of these Discuss
- 10. In a circular lawn, there is a 16 m long path in the form of a chord. If the path is 6 m away from the center of the lawn, then find the radius of the circular lawn.
Options- A. 16 m
- B. 6 m
- C. 10 m
- D. 8 m Discuss
More questions
Correct Answer: 1 and 1
Explanation:
The HCF of m and n is 1, so m and n are prime number.
Let m = 7 and n = 5 ? m + n = 12
HCF of(m + n)and m = HCF of 12 and 7 = 1
Similarly, HCF of (m - n) and n = 1
Correct Answer: 48
Explanation:
Let be the ten's digit be x and unit's digit be y.
So the two digit number = 10x + y ( where x > y )
According to question
x + y = 14 ....(i)
x - y = 2 ....(ii)
Solving Eqs. (i) and (ii), we get
x = 8 and y = 6
? Required product = 8 x 6 = 48
Correct Answer: 10.8
Explanation:
Increase in 3 years over 100 = 100 x {1 + 7/(2 x 100)}3
= (100 x 207/200 x 207/200 x 207/200)
= (200 + 7)3 / 80000
= 88869743 / 80000 = 110.8718
Required increase % = (110.8 - 100)% = 10.8%
Correct Answer: 2
Explanation:
? 2log4x = 1 + log4(x-1)
? log4x2 = log44 + log4(x-1)
? x2 = 4(x-1)
? x2 - 4x + 4 = 0
? (x-2)2 = 0
? x = 2
Correct Answer: 77/9%
Explanation:
Let the rate of interest allowed by bank be r%
According to the question,
[(12000 x 5 x 10)/100] - [(12000 x 3 x r)/100] = 3320
? 6000 - 360r = 3320
? 360r = 6000 - 3320 = 2680
? r = 2680/360 = 74/9%
Correct Answer: 0.4771
Explanation:
Given log90 = 1.9542
? log(32 x 10) = 1.9542
? 2log 3 + log 10 = 1.9542
? log 3 = 0.9542 / 2 = 0.4771
Correct Answer: 2/7
Explanation:
A leap year has 366 days = 52 weeks + 2 days. These 2 days can be (Sunday, Monday, Wednesday) .... or (Saturday, Sunday). Out of these total 7 out comes there are 2 cases favourable to the desired event i, e. (Sunday, Monday) and (Monday, Tuesday)
? Required probability = 2/7
Correct Answer: ab a+b
Explanation:
Correct Answer: None of these
Explanation:
Let C(O, r) is a circle and let M is a point within it where O is the centre and r is the radius of the circle.
Let CD is another chord passes through point M.
We have to prove that AB < CD.
Now join OM and draw OL perpendicular to CD.
In right angle triangle OLM,
OM is the hypotenuse.
So OM > OL
? chord CD is nearer to O in comparison to AB.
? CD > AB
? AB < CD
So all chords of a circle of a circle at a given point within it, the smallest is one which is bisected at that point.
Hence required answer will be option D .
Correct Answer: 10 m
Explanation:
From given figure , we can see that
Let AB = 16 m , OM = 6 m , AM = BM = 8 m and OA = r
In triangle AMO ,
By pythagoras theorem ,
OA2 = AM2 + OM2
OA2 = 82 + 62 = 64 + 36
OA2 = 100 ? OA = ? 100 = 10
? OA = r = 10 m
The radius of the circular lawn = 10 m
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