1. A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
A. Rs. 2000
B. Rs. 10,000
C. Rs. 15,000
D. Rs. 20,000
Answer: Option (C)
Explanation:
Principal = Rs. ([latex]\frac{100 \times 5400}{12 \times 3}[/latex])= Rs. 15000.
2. Due to the sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?
A. 63 ft
B. 72 ft
C. 54 ft
D. 48 ft
Answer: Option (C)
Explanation:
3. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
A. 4830
B. 5120
C. 6420
D. 8960
Answer: Option (B)
Explanation:
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) [latex]{m}^{3}[/latex] = 5120 [latex]{m}^{3}[/latex].
4. If log 2 = 0.30103, the number of digits in 264 is:
Answer: Option C
Explanation:
log (264) = 64 x log 2
= (64 x 0.30103)
= 19.26592
Its characteristic is 19.
Hence, then a number of digits in 264 is 20.
5. X, Y, and Z are the three contestants in one km race. If X can give Y a start of 52 meters and X can also give Z a start of 83 meters, how many meters start Y can give Z?
A. 33.3 m
B. 33 m
C. 32 m
D. 32.7 m
Answer: Option D
Explanation :
While X runs 1000 metre, Y runs (1000-52)=948 metre and Z runs (1000-83)=917 metre
i.e., when Y runs 948 meters, Z runs 917 meters
When Y runs 1000 metre, Z runs ([latex]\frac{917}{948}[/latex])×1000 = 967.30 metre
i.e., Y can give Z (1000-967.30) = 32.7 meters.
6. 6156 ÷ √? × 53 = 4028
A. 6889
B. 6241
C. 5929
D. 6561
None of these
Answer: D
Solution:
([latex]\frac{6153 \times 53}{\sqrt{?}}[/latex]) = 4028
? = 80.96 ≈ 81
? = 6561.
7. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
A. 50 km
B. 56 km
C. 70 km
D. 80 km
Answer: Option A
Explanation:
Let the actual distance traveled be x km.
Then,([latex]\frac{x}{10}[/latex]) = ([latex]\frac{x + 20}{14}[/latex])
14x = 10x + 200
4x = 200
x = 50 km.
8. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Answer: Option B
Explanation:
There is a meal for 200 children. 150 children have taken the meal.
The remaining meal is to be catered to 50 children.
Now, 200 children 120 men.
50 children =([latex]\frac{120}{200}[/latex]) x 50 = 30 men.
9. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
A. 32
B. 48
C. 36
D. 60
E. 120
Answer: Option C
Explanation:
There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6)
Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = 3P3 = 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = 3P3 = 3! = 6.
Total number of ways = (6 x 6) = 36.
10. (256)0.16 x (256)0.09 = ?
A. 4
B. 16
C. 64
D. 256.25
Answer: Option A
Explanation:
(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)
= (256)0.25
= (256)(25/100)
= (256)(1/4)
= (44)(1/4)
= 44(1/4)
= 41
= 4
11. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
A. 20 hours
B. 25 hours
C. 35 hours
D. Cannot be determined
E. None of these
Answer: Option C
Explanation:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take ([latex]\frac{x}{2}[/latex]) and ([latex]\frac{x}{4}[/latex]) hours respectively to fill the tank.
([latex]\frac{1}{x}[/latex]) + ([latex]\frac{2}{x}[/latex]) + ([latex]\frac{4}{x}[/latex]) =([latex]\frac{1}{5}[/latex]) 1
([latex]\frac{7}{x}[/latex]) = ([latex]\frac{1}{5}[/latex])
x = 35 hrs.
13. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance traveled downstream in 12 minutes is:
A. 1.2 km
B. 1.8 km
C. 2.4 km
D. 3.6 km
Answer: Option D
Explanation:
Speed downstream = (15 + 3) kmph = 18 kmph.
Distance travelled = 18 x ([latex]\frac{12}{60}[/latex])km
= 3.6 km.
14. On dividing a number by 357, we get 39 as the remainder. On dividing the same number 17, what will be the remainder?
Answer: Option C
Explanation:
Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
15. A began a business with Rs. 85,000. He was joined afterward by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3: 1?
A. 4 months
B. 5 months
C. 6 months
D. 8 months
Answer: Option D
Explanation:
Suppose B joined for x months. Then,
Then, ([latex]\frac{1800\times 12}{42500\times x}[/latex])=([latex]\frac{3}{1}[/latex])
x = ([latex]\frac{1800\times 12}{42500\times 3}[/latex])
= 8.
So, B joined for 8 months.
16. The fourth proportional to 5, 8, 15 is:
Answer: Option B
Explanation:
Let the fourth proportional to 5, 8, 15 be x.
Then, 5: 8: 15: x
5x = (8 x 15)
x = ([latex]\frac{(8 x 15)}{5}[/latex]) = 24.
17. Find the lowest common multiple of 24, 36 and 40.
A. 120
B. 240
C. 360
D. 480
Answer: Option C
Explanation:
2 | 24 - 36 - 40
--------------------
2 | 12 - 18 - 20
--------------------
2 | 6 - 9 - 10
-------------------
3 | 3 - 9 - 5
-------------------
| 1 - 3 - 5
L.C.M. = 2 x 2 x 2 x 3 x 3 x 5 = 360.
18. The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
A. Rs. 60
B. Rs. 108
C. Rs. 110
D. Rs. 112
Answer: Option B
Explanation:
P.W. = Rs. (540 - 90) = Rs. 450.
S.I. on Rs. 450 = Rs. 90.
S.I. on Rs. 540 = Rs. ([latex]\frac{90}{450}[/latex]) x 540 = Rs. 108.
B.D. = Rs. 108.
Compound Interest
[latex]1600 \times (1 + \frac{5}{2 \times100})^{2}[/latex]
19. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
A. 6.06%
B. 6.07%
C. 6.08%
D. 6.09%
Answer: Option D
Explanation:
Amount of Rs. 100 for 1 year
when compounded half-yearly = Rs. [latex]100 \times (1 + \frac{3}{100})^{2} [/latex]
Effective rate = (106.09 - 100)% = 6.09%
20. A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Answer: Option C
Explanation:
Area of the field = 680 sq. feet.
Length of the adjacent sides are
20 feet and ([latex]\frac{680}{20}[/latex]) = 34 feet.
Required length of the fencing = 20 + 34+ 34 = 88 feet
21. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A. 8 hours
B. 10 hours
C. 12 hours
D. 24 hours
Answer: Option C
Explanation:
A's 1 hour's work = ([latex]\frac{1}{4}[/latex])
(B + C)'s 1 hour's work = ([latex]\frac{1}{3}[/latex])
(A + C)'s 1 hour's work = ([latex]\frac{1}{2}[/latex])
(A + B + C)'s 1 hour's work = ([latex]\frac{1}{4}[/latex] + [latex]\frac{1}{3}[/latex]) = ([latex]\frac{7}{12}[/latex])
B's 1 hour's work = ([latex]\frac{7}{12}[/latex] - [latex]\frac{1}{2}[/latex]) = ([latex]\frac{1}{12}[/latex])
Therefore B alone will take 12 hours to do the work.
22. Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
A. 1: 3
B. 2: 3
C. 3: 4
D. 4: 5
Answer: Option B
Explanation:
By the rule of allegation:
Required ratio = 60 : 90 = 2 : 3.
23. 617 + 6.017 + 0.617 + 6.0017 = ?
A. 6.2963
B. 62.965
C. 629.6357
D. None of these
Answer: Option C
Explanation:
617.00
6.017
0.617
+ 6.0017
--------
629.6357
---------
24. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
A. [latex]\frac{1}{10}[/latex]
B. [latex]\frac{2}{5}[/latex]
C. [latex]\frac{2}{7}[/latex]
D. [latex]\frac{5}{7}[/latex]
Answer: Option C
Explanation:
P (getting a prize) = [latex]\frac{10}{10 + 25}[/latex] = [latex]\frac{10}{35}[/latex] = [latex]\frac{2}{7}[/latex].
25. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R are Rs. 5200. The monthly income of P is:
A. 3500
B. 4000
C. 4050
D. 5000
Answer: Option B
Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
26. A man invested Rs. 1552 in stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
A. 7.5%
B. 8%
C. 9.7%
D. None of these
Answer: Option B
Explanation:
By investing Rs. 1552, income = Rs. 128.
By investing Rs. 97, income = Rs. ([latex]\frac{128}{1552}[/latex] x 97 ) = Rs. 8.
Dividend = 8%
3. The square root of 64009 is:
A. 253
B. 347
C. 363
D. 803
Answer: Option A
Explanation:
2|64009( 253
|4
|----------
45|240
|225
|----------
503| 1509
| 1509
|----------
| X
|----------
[latex]\sqrt{64009}[/latex] = 253.
27. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A. 14 years
B. 18 years
C. 20 years
D. 22 years
Answer: Option D
Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
28. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
A. 16 years
B. 18 years
C. 28 years
D. 24.5 years
E. None of these
Answer: Option D
Explanation:
Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.
[latex]\frac {x - 7}{x}[/latex] = [latex]\frac {7}{9}[/latex]
9x - 63 = 7x
2x = 63
x = 31.5
Hence, Sachin's age =(x - 7) = 24.5 years.
29. The least perfect square, which is divisible by each of 21, 36 and 66 is:
A. 213444
B. 214344
C. 214434
D. 231444
Answer: Option A
Explanation:
L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 2[latex]^{2}[/latex] x 3[latex]^{2}[/latex] x 7[latex]^{2}[/latex] x 11[latex]^{2}[/latex]= 213444
30. The cost price of a Rs. 100 stock at 4 discount, when brokerage is[latex]\frac {1}{4}[/latex]% is:
A. Rs. 95.75
B. Rs. 96
C. Rs. 96.25
D. Rs. 104.25
Answer: Option C
Explanation:
C.P. = Rs. (100 - 4 + [latex]\frac {1}{4}[/latex])= Rs. 96.25
31. In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
A. 67 kg.
B. 68 kg.
C. 69 kg.
D. Data inadequate
E. None of these
Answer: Option A
Explanation:
Let Arun's weight by X kg.
According to Arun, 65 < X < 72
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required average = [latex]\frac {66 + 67 + 68}{3}[/latex] = [latex]\frac {201}{3}[/latex] = 67 kg.
32. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A. [latex]\frac {1}{13}[/latex]
B. [latex]\frac {3}{13}[/latex]
C. [latex]\frac {1}{4}[/latex]
D. [latex]\frac {9}{52}[/latex]
Answer: Option B
Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = [latex]\frac {12}{52}[/latex] = [latex]\frac {3}{13}[/latex].
33. Which of the following is equal to 3.14 x 10[latex]^{6}[/latex] ?
A. 314
B. 3140
C. 3140000
D. None of these
Answer: Option C
Explanation:
3.14 x 10[latex]^{6}[/latex] = 3.14 x 1000000 = 3140000.
34. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
Answer: Option B
Explanation:
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y = [latex]\frac {1}{8}[/latex] and 3x + 7y = [latex]\frac {1}{10}[/latex].
Solving the two equations, we get: x = [latex]\frac {11}{400}[/latex] , y = [latex]\frac {1}{400}[/latex]
1 woman's 1 day's work = [latex]\frac {1}{400}[/latex] .
10 women's 1 day's work = ([latex]\frac {1}{400}[/latex] x 10) = [latex]\frac {1}{40}[/latex] .
Hence, 10 women will complete the work in = 40 days.
35. A boat having a length of 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
A. 12 kg
B. 60 kg
C. 72 kg
D. 96 kg
Answer: Option B
Explanation:
Volume of water displaced = (3 x 2 x 0.01) m[latex]^{3}[/latex]
= 0.06 m[latex]^{3}[/latex].
Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
36. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
A. 6.06%
B. 6.07%
C. 6.08%
D. 6.09%
Answer: Option D
Explanation:
Amount of Rs. 100 for 1 year
when compounded half-yearly = Rs. (100 x (1 + [latex]\frac {3}{100})^{2}[/latex]) = Rs. 106.09
Effective rate = (106.09 - 100)% = 6.09%
37. The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker's discount is:
A. Rs. 37
B. Rs. 37.62
C. Rs. 34.38
D. Rs. 38.98
Answer: Option B
Explanation:
B.G. =[latex]\frac {(T.D.)^{2}}{P.W.}[/latex] = Rs.[latex]\frac {36 \times 36}{800}[/latex]= Rs. 1.62
B.D. = (T.D. + B.G.) = Rs. (36 + 1.62) = Rs. 37.62
38. The sum of the three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5: 8, then the second number is:
Answer: Option B
Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 = (5 x [latex]\frac {3}{5}[/latex]) : (8 x [latex]\frac {3}{5}[/latex]) = 3 : [latex]\frac {24}{5}[/latex]
A : B : C = 2 : 3 : [latex]\frac {24}{5}[/latex] = 10 : 15 : 24
B = (98 x [latex]\frac {15}{49}[/latex]) = 30.
39. A began a business with Rs. 85,000. He was joined afterward by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3: 1?
A. 4 months
B. 5 months
C. 6 months
D. 8 months
Answer: Option D
Explanation:
Suppose B joined for x months. Then,
Then, [latex]\frac {85000 \times 12 }{42500 \times x}[/latex] = [latex]\frac {3}{1}[/latex]
x = [latex]\frac {85000 \times 12 }{42500 \times 3}[/latex] = 8.
So, B joined for 8 months.
40. How many 3 digit numbers are divisible by 6 in all?
A. 149
B. 150
C. 151
D. 166
Answer: Option B
Explanation:
Required numbers are 102, 108, 114, ... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then,
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150.
41. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along with the current in 10 minutes. How long will it take to go 5 km in stationary water?
A. 40 minutes
B. 1 hour
C. 1 hr 15 min
D. 1 hr 30 min
Answer: Option C
Explanation:
Rate downstream = [latex]\frac {1}{10}[/latex] x 60 km/hr = 6 km/hr.
Rate upstream = 2 km/hr.
Speed in still water = [latex]\frac {1}{2}[/latex] (6 + 2) km/hr = 4 km/hr.
Required time = [latex]\frac {5}{4}[/latex]hrs = 1 [latex]\frac {1}{4}[/latex] hrs = 1 hr 15 min.
42. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
A. 10 min. 20 sec.
B. 11 min. 45 sec.
C. 12 min. 30 sec.
D. 14 min. 40 sec.
Answer: Option D
Explanation:
Part filled in 4 minutes = 4 ([latex]\frac {1}{15}[/latex] + [latex]\frac {1}{20}[/latex]) = [latex]\frac {7}{15}[/latex].
Remaining part = (1 - [latex]\frac {7}{15}[/latex]) = [latex]\frac {8}{15}[/latex].
Part filled by B in 1 minute = [latex]\frac {1}{20}[/latex]
[latex]\frac {1}{20}[/latex] : [latex]\frac {8}{15}[/latex] :: 1 : x
x = ([latex]\frac {8}{15} \times 1 \times 20[/latex]) = 10 [latex]\frac {2}{3}[/latex]min = 10 min. 40 sec.
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
43. (17)[latex]^{3.5}[/latex] x (17)[latex]^{?}[/latex] = 17[latex]^{8}[/latex]
A. 2.29
B. 2.75
C. 4.25
D. 4.5
Answer: Option D
Explanation:
Let (17)[latex]^{3.5}[/latex] x (17)[latex]^{x}[/latex] = 17[latex]^{8}[/latex]x.
Then, (17)[latex]^{3.5}[/latex] + x = 17[latex]^{8}[/latex].
3.5 + x = 8
x = (8 - 3.5)
x = 4.5
44. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
A. 10080
B. 4989600
C. 120960
D. None of these
Answer: Option C
Explanation:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
A number of ways of arranging these letters = [latex]\frac {8!}{(2!)(2!)}[/latex] = 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
A number of ways of arranging these letters = [latex]\frac {4!}{2!}[/latex] = 12.
Required number of words = (10080 x 12) = 120960.
45. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Answer: Option B
Explanation:
There is a meal for 200 children. 150 children have taken the meal.
The remaining meal is to be catered to 50 children.
Now, 200 children = 120 men.
50 children = [latex]\frac {120}{200}[/latex] x 50 = 30 men.
46. A farmer traveled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance traveled on foot is:
A. 14 km
B. 15 km
C. 16 km
D. 17 km
Answer: Option C
Explanation:
Let the distance traveled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, [latex]\frac {x}{4}[/latex] + [latex]\frac {(61 -x)}{9}[/latex] = 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
47. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds
Answer: Option A
Explanation:
Let the total number of shots be x. Then,
Shots fired by A = [latex]\frac {5}{8}[/latex]x
Shots fired by B = [latex]\frac {3}{8}[/latex]x
Killing shots by A = [latex]\frac {1}{3}[/latex] of [latex]\frac {5}{8}[/latex] x = [latex]\frac {5}{24}[/latex]x
Shots missed by B = [latex]\frac {1}{2}[/latex] of [latex]\frac {3}{8}[/latex] x = [latex]\frac {3}{16}[/latex]x
[latex]\frac {3 \times x}{16}[/latex] = 27 or x = [latex]\frac {27 \times 16}{3}[/latex] = 144.
Birds killed by A = [latex]\frac {5x}{24}[/latex] = [latex]\frac {5}{24}[/latex] x 144 = 30.
48. A can run 22.5 m while B runs 25 m. In a kilometer race, B beats A by:
A. 100 m
B. 111[latex]\frac {1}{9}[/latex] m
C. 25 m
D. 50 m
Answer: Option A
Explanation:
When B runs 25 m, A runs [latex]\frac {45}{2}[/latex] m.
When B runs 1000 m, A runs ([latex]\frac {45}{2}[/latex] x [latex]\frac {1}{25}[/latex] x 1000) m = 900 m.
B beats A by 100 m.
49. If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
Answer: Option B
Explanation:
[latex]log_{10}[/latex] 5 + [latex]log_{10}[/latex] (5x + 1) = [latex]log_{10}[/latex] (x + 5) + 1
[latex]log_{10}[/latex] 5 + [latex]log_{10}[/latex] (5x + 1) = [latex]log_{10}[/latex] (x + 5) + [latex]log_{10}[/latex] 10
[latex]log_{10}[/latex] [5 (5x + 1)] = [latex]log_{10}[/latex] [10(x + 5)]
5(5x + 1) = 10(x + 5)
5x + 1 = 2x + 10
3x = 9
x = 3.
50. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A. 720
B. 900
C. 1200
D. 1800
Answer: Option C
Explanation:
2(15 + 12) x h = 2(15 x 12)
h = [latex]\frac{180}{27}[/latex] m = [latex]\frac{20}{3}[/latex] m.
Volume = ([latex]{15 \times 12 \times \frac {20}{3}}[/latex]) m[latex]^{3}[/latex] = 1200 m[latex]^{3}[/latex].