1. The ratio of present ages of three persons are 6 : 9 : 11.Ten years ago, the sum of their ages was 48. Find the average of their present ages (in years).
2. 64 women can do a work in 36 days. 54 men can complete the same work in 21 days. Find the ratio between the working capacity of a Man and a women?
3. The average weight of A, B and C is 64 kg. If the average weight of A and B be 54 kg and that of B and C be 58 kg, then the weight of B is:
4. Two taps X and Y can fill a Tank in 30 and 60 minutes respectively. There is a third exhaust tap Z at the bottom of tank. If all taps are opened at the same time, the Tank will be full in 50 minutes. In what time can exhaust tap Z empty the cistern when full?
5. Moradabad is at a distance of 340 km from New delhi. A train starts from New delhi to Moradabad at 6 P.M. with a speed of 60 km/hr. Another train starts from Moradabad to New delhi at 7 P.M. with a speed of 80 km/hr. At what distance from New delhi will the two trains cross each other and also find the time when they cross each other?
6. Arun alone can do a piece of work in 9 days and Bimal alone in 12 days. Arun and Bimal undertook to do it for Rs. 4800. With the help of Chintu, they completed the work in 5 days. How much is to be paid to chintu
7. A dealer bought an item at 10% discount on its original price. He sold it at 35% more than the original price. What percentage profit did he get?
8. Price register an increase of 10% on food grains and 15% on other items of expenditure. If the ratio of expenditure of an employee on food grains and other items be 2:5, by how much should his salary be increased in order that he may maintain the same level of consumption as before? Assume that there is no saving our of his monthly salary of Rs 2590.
9. The ratio of the present ages of Arnab and Sanjana is 13:17 respectively. Four years ago the respective ratio of their ages was 11 : 15. What will be the respective ratio of their ages six years hence?
10. The average age of 80 boys in a class is 15 years. The average age of a group of 15 boys in the class is 16 years and the average age of another 25 boys in the class is 14 years. What is the average age of the remaining boys in the class?
Directions (Q. 11-15): In each of the following questions two equations are given. You have to solve the equations and give answer.
11). I. 4x² – 8x + 3 = 0
II. 2y² – 7y + 6 = 0
12). I. x² + x - 6 = 0
II. 2y² – 13y + 21 = 0
13). I. x² – x - 6 = 0
II. 2y² + 13y + 21 = 0
14). I. x² = 4
II. y² + 6y + 9 = 0
15). I. 2x + 3y = 4
II. 3x + 2y = 11
Directions (Q. 16-20): What value should come in place of question mark (?) in the following questions?
16). (2465 ÷ 49.3)% of 6872 + ? % of 480 = 5836
17). 125% of 260 + ? % of 560 = 500
18). 430% of 650 + (?) of 4.5 – 20% of 2220 = 7292
19). 1.4 × 625 + 4.2 ÷ 0.7 + 325 × 9.8 = (?)2 – 159
20). 45% of 180 + ?% of 160 = 50% of 274
Directions (Q. 21-25): what will be come in place of question mark (?) in the following number series?
21). 14 8 7 11.5 22 ?
22). 8 14 25 46 82 ?
23). 13 14 30 93 ? 1885
24). 65 70 63 74 61 ?
25). 9 11 16 33 98 ?
26) If the ratio of interest rate of E to that of D is 2:3 then what is the Principal(P) of D?
A. 15000
B. 20000
C. 35000
D. 25000
E. 30000
27) If the interest is compounded yearly for three years then what is the amount to be earned by C?
A. 23497.28
B. 20497.28
C. 22597.28
D. 22697.28
E. 22497.28
28) What is the Simple Interest(SI) of B ? If the ratio of Principal of C to that of B is 4:5 and the rate of interest is 10% more than that of C.
A. 3300
B. 4400
C. 2200
D. 1100
E. 5500
29) If the Principal(P) of A is 20% more than that of E, then What is the amount of A?
A. 12694.60
B. 16584.60
C. 12584.80
D. 12484.80
E. 15684.60
30) If amount of D equals to five times that of his Principal then what is the Rate of Interest(%)?
A. 122.22%
B. 144.44%
C. 133.33%
D. 155.55%
E. None of the Above
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Solutions:
Answer.1.E
Let their present ages be 6x, 9x and 11x years respectively.
Then, (6x – 10) + (9x – 10) + (11x – 10) = 48
26x = 78
x = 3
Their present ages are 6x = 18 years, 9x = 27 years and 11x = 33 years respectively.
hence, Required Average = (18+ 27+ 33)/3 = 78/3 = 26 years
Answer.2.B
(64 x 36) womens can complete the work in 1 day.
1 day’s work of 1 Woman’s = 1/2304
(54 x 21) Men can complete the work in 1 day.
1 day’s work of 1 Man‘s = 1/1134
therefore,
Req. ratio = 1/1134 : 1/2304 = 128:63
Answer.3.D
A + B + C = (64 x 3) = 192 …. (i)
A + B = (54 x 2) = 108 …. (ii)
B + C = (58 x 2) = 116 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 224 …. (iv)
Subtracting (i) from (iv), we get : B = 224-192= 32.
hence, B’s weight = 32 Kgs.
Answer.4.A
Let tap C will empty the tank in ‘t’ minutes
Here, X = 30, Y = 60 and Total time to fill tank = 50 minutes
C can empty the full tank in = (XYZ /YZ +ZX –XY) Minutes
= ( 30*60*50/ ( 60*50 + 30*50 -30*60)
= 90000/2700 = 10/3 Minutes
Answer.5.C
Speed of train from new Delhi to Moradabad (s1) = 60,
Speed of train from Moradabad to new delhi (s2) = 80,
T = time from 6 P.M. to 7 P.M. = 1 hr
Distance of meeting point from New delhi= S1 {( d +S2 t) / (S1 +S2)} km
= 60 {( 340 + 80X1) / (60+80)} = 180 km
Time of their meeting = {( d +S2 t) / (S1 +S2)}
{( 340 + 80X1) / (60+80)}
3 Hrs after 6 PM
i.e. 9:00 PM
Answer.6.B
Chintu’s 1 day’s work = 1/5 – ( 1/9 + 1/12) = (1/5 – 7 /36) = 1/180
hence, Ratio of their wages = Arun :Bimal :Chintu =1/9 : 1/12 : 1/ 180
= 20:15:1
hence,
Chintu’s Share=4800 * (1/36) = 133.33 Rs.
Answer.7.(D)
Let the original price to be Rs 100.
So he bought it at 10% discount ieRs 90 and
sells it at 35% more than the original rate ieRs 135.
Actual profit is 135- 90=Rs 45
So % profit =45/90×100=50%
Answer.8.(A)
By the method of allegation
(15-x)/(x-10)=2/5
Or, 75- 5x=2x-20
Or, 7x=95
Or, x=13.57%
Answer.9.(E)
Let the present ages of Arnab and Sanjana be 13x and 17x years respectively.
?(13x-4)/(17x-4)=11/15
187x – 44=195x-60
195x-187x = 60-44
8x=16
x=2
Required ratio =(13×2+6):(17×2+6) =32 : 40 = 4 : 5
Answer.10.(A)
Let the required average age be x years.
80×15=15×16+25×14+40×x
40x=1200-240-350=610
hence, x=610/40=15.25 years
11). B) From equation I:
4x2 -8x+3 = 0
or, 4x2-6x-2x+3=0
or, 2x(2x -3)-1(2x -3) = 0
or, (2x -1)(2x -3) = 0
If, 2x -1 = 0 à x =1/2
and if 2x - 3 =0 à x = 3/2
x =1/2 or 3/2
From equation II:
2y2 - 7y +6 = 0
or,2y2-4y-3y+6 = 0
or, (2y-3) (y-2)=0
If2y-3 =0 à y=3/2
and if y – 2 = 0à y=2
y =3/2 or 2
Hence, x ≤ y
12). A) From equation I:
x2+ x - 6 = 0
or, x2 – 2x + 3x – 6 = 0
or, x(x -2) +3(x - 2) = 0
(x - 2) (x + 3) = 0
If, x - 2 =0 à x= 2 and x + 3 = 0 à x = -3 or 2
From equation II:
2y2 – 13y + 21 = 0
or, 2y2 – 6y – 7y + 21 = 0
or, 2y(y-3) -7(y-3) = 0
or, (2y - 7) (y - 3) = 0
If, 2y- 7= 0 à y = 7/2 and if y-3 = 0 à y = 3
y = 3 or 7/2 Hence, x <y
13). E) From equation I:
x2 – x – 6 = 0
or, x2 – 3x + 2x – 6 = 0
or, x(x-3) + 2(x-3) = 0
or, (x-3)(x+2) = 0
if, x-3 = 0 à x =3 and if x+2 = 0 à x = -2
x = -2 or 3
From equation II:
2y2 +13y+21=0
or, 2y2 +6y+7y+21 = 0
or,2y(y+3)+7(y+3)=0
or, (2y+7)(y+3) = 0
If, 2y + 7 = 0 à y = -(7/2)and if y + 3 =0 à y =-3
Hence x > y
14). E) From equation I:
x2 = 4
x = √4 à x = ±2
from equation II:
y2 + 6y + 9 = 0
or, y2 + 3y + 3y + 9 = 0
or,y (y + 3)+3(y+3) = 0
or, (y+3) (y+3)=0
or, y+3 = 0
Hence x > y
15). E) From I and II we get y =-2 and x = 5
x > y
16). E) ? x 4.80 = 5836 – (2465 ÷ 49.3)% of 6872 = 5836 – 50% of 6872
= 5836 –(1/2) x 6872 = 5836 – 3456 = 2400
? = 2400/4.80 = 500
17). B) ?% of 560 = 500 – (100% of 260 + 25% of 260) = 500 – (260 + 65) = 500 – 325 = 175
or, ? x 5.60 = 175
? = 17500/560 = 1750/56 = 125/4 = 31.25
18). B) ? x 4.5 = 7292 – (400% of 650 + 30% of 650) + (20% of 2220)
= 7292 – (2600 + 195) + 444
= 7736 – 2795 = 4941
? = 4941/4.5 = 49410/45 = 5490/5 = 1098
19). C) (?)2 = 1.4 x 625 + 4.2 ÷ 0.7 + 325 x 9.8 + 159 = 875 + 6 + 3185 + 159 = 4225 ? =√4225 = 65
20). A) ? × 1.60 = (1/2) x 274 - 45 x1.8 ,
= 137 - 81 = 56
? = 56/1.6 = 35
21). E) The series is x0.5 + 1, ×1 - 1, ×1.5 + 1, ×2 – 1, ×2.5 + 1, …..
Ie 14 × 0.5 + 1 = 8, 8 × 1 - 1 = 7, 7 × 1.5 + 1 = 11.5, 11.5 × 2 - 1 = 22, 22 × 2.5 + 1 = 56,
22). C)
23). D) The series is x1 + 1, x2 + 2, ×3 + 3, x4 + 4, x5 + 5, ...
ie 13 x 1 + 1 = 14, 14 x 2 + = 30, 30 x 3 + 3 = 93, 93 x 4 + 4 = 376, 376 x 5 + 5 = 1885,
24). A) The pattern is -2, +4 (Alternate) The series is a combination of two series
25). B) The series is +12 + 1, +22 + 1, +42 + 1, +82 + 1, +162 + 1, ...
ie 9 + 12 + 1 = 11, 11 + 22 + 1 16, 16 + 42 + 1 = 33, 33 + 82 + 1 = 98, 98 + 162 + 1 = 355,
26) Answer – D. 25000
Explanation :
R(%) = 4*3/2 = 6
Principal – x
x + (x*3*6/100) = 29500
x = 25000
27) Answer – E. 22497.28
Explanation :
Amount = P(1 + (R/100)^3)
A = 20000 * 1.04 * 1.04 * 1.04
A = 22497.28
28) Answer – B. 4400
Explanation :
P = 5/4 * 20000 = 25000
The rate of interest is 10% more than that of C.
R(%) = 4 + (4*(10/100)) = 4.4 %
SI = [25000 * 4.4 * 4]/100 = 4400
29) Answer – D. 12484.80
Explanation :
Principal(P) of A = 10000 * 120/100 = 12000
A = P(1 + (R/100)^N) = 12000(1 + (2/100)^2) = 12484.80
30) Answer – C. 133.33%
Explanation :
Amount of D = Rs.29500
Principal – x
Amount of D = 5x
5x = 29500 => x= 5900
SI = 29500 – 5900 = 23600
R = 23600 * 100 / 5900 * 3 = 133.33%
31) D
32) C
33) E
34) A
35) B
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