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Application Sums
1) 12 boys and 18 girls can complete a work in 6 days. 12 girls can complete the work in 18 days. 12 boys and 18 girls started the work 4 days after 4 boys left. In how many days, the remaining people will complete the work?
a) 12/5
b) 36/5
c) 48/5
d) 24/5
e) None of these
2) Express A leaves Chennai at 5 a.m. and reaches Mumbai at 9 a.m. another train Express B leaves Mumbai at 7 a.m. and reaches Chennai at 10:30 a.m. At what time they cross each other after 7 a.m.?
a) 56 min
b) 60 min
c) 14 min
d) 15 min
e) None of these
3) A man runs at a uniform speed and covers 36 km. Had the speed been 6 kmph less, it would have taken one more hour to complete the distance.
From the statement given in the above question which of the following can be determined.
A) Initial speed of the man
B) Initial time taken
C) Speed of the man in the latter case
D) Time taken by the man in the latter case
a) Only A
b) Only A & C
c) Only D
d) B & D
e) All of these
4) A boat takes 150 mins less to travel 40 km downstream than to travel the same distance upstream. If the speed of the stream is 4, what is the time taken to travel 25 km upstream?
a) 5/8 hr
b) 25/16 hr
c) 25/8 hr
d) 5/16 hr
e) None of these
5) Pipes A and B can fill the tank in 48/11 min but because of the drainage pipe C, it is being filled by 24/5 min. If C can drain off 15 l/min, what is the capacity of the tank?
a) 360 litres
b) 320 litres
c) 480 litres
d) 720 litres
e) None of these
Caselet
Directions (6-10): Study the following information carefully and answer the questions given below?
Ram’s age 2 years ago and Bala’s age 5 years ago are in the ratio 6: 5. The sum of their ages is 95, as Ram is (A) years old and Bala is (B) years old. Ram and Bala decided to keep them young by doing swimming. Ram swims 20 km upstream and returns back where current speed is 5 kmph. Swimming in upstream takes 1 hour more than downstream. Bala swims in still water at (C) kmph which is twice that of Ram. While coming back from swimming pool, they sell their cycles at a profit of (D)% after giving a discount of 10% and the markup is 25%.
The profit earned is lent at a rate of 4% compounded annually for 2 years which amounts to 43264. The same principal is lent at 15% simple interest for 2 years amounts to (E).
After reaching home, they decided to enter into partnership. Ram invests Rs.900 for 6 months and Bala invests (F) for the whole year. At the end of one year the profit ratio of Ram and Bala is 15: 13.
6) What will come in place of A and B?
a) 40, 35
b) 35, 40
c) 45, 50
d) 50, 45
e) None of these
7) What will come in place of C?
a) 60 kmph
b) 15 kmph
c) 90 kmph
d) 30 kmph
e) None of these
8) What will come in place of D?
a) 37.5 %
b) 25%
c) 16.667%
d) 12.5%
e) None of these
9) What will come in place of E?
a) 24000
b) 36000
c) 10000
d) 12000
e) None of these
10) What will come in place of F?
a) 460
b) 490
c) 360
d) 390
e) None of these
Answers :
Directions (1-5) :
1) Answer: A
(12b + 18g) * 6 = 12g * 18
12b + 18g = 36g
12b = 18g
b = 3/2g
(12b + 18g) * 4 + (8b +18g) * D = 12g * 18
b = 3/2g, so
36g * 4 + 30g * D = 12g * 18
24g + 5g * D = 36g
D = 12/5
2) Answer: A
s1 = x/4, s2 = 2x/7, t1 = y + 2, t2 = y
x/4 * (y + 2) + 2x/7 * (y) = x
(y + 2)/4 + 2y/7 = 1
y = 14/15
Required time = 14/15 * 60 = 56 min
3) Answer: E
36 = s * t —– 1
36 = (s – 6) * (t + 1) —– 2
From 1 and 2,
36/(s – 6) – 36/s = 1
s2 – 6s – 216 = 0
s = -12, 18
s = 18
t = 36/18 = 2
In latter case, s – 6 = 12
t + 1 = 3
Hence, we can find all from the given statement.
4) Answer: C
Speed of the boat = x
40/(x – 4) – 40/(x + 4) = 150/60 hr
x2 – 16 = 128
x = 12, -12
Now for 25 km, 25 = (12 –Â Â 4) * t
t = 25/8 hrs
5) Answer: D
1/A + 1/B = 11/48 —– 1
1/A + 1/B – 1/C = 5/24 —— 2
From 1 and 2,
1/C = 1/48
C drain off 15l/min,
48 * 15 = 720 litres
Directions (6-10) :
6) Answer: D
5x + 5 + 6x + 2 = 95
x = 8
Ram: 6x + 2 = 50
Bala: 5x + 5 = 45
7) Answer: D
20/(x – 5) – 20/(x + 5) = 1
x2 = 225
x = 15
2x = 30 kmph
8) Answer: D
Let us take cost price of the bicycle be Rs.100
MP = 100 * 125/100 = Rs.125
SP = 125 * (100 – 10)/100 = Rs.112.5
Required percentage = (112.5 – 100)/100 * 100 = 12.5%
9) Answer: D
Amount = P (1 + R/100)2
43264 = P (1 + 4/100)2
43264 * 100/104 * 100/104 = 40000
Simple interest = PNR/100
= (40000 * 15 * 2)/100 = Rs. 12000
10) Answer: D
Profit ratio of Ram and Bala = (900 * 6)/(x * 12) = 15/13
x = 390
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