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Application Sums
Directions (1-10) :
1) Three persons P, Q and R decided to work in such a way that P and Q work together on first day, R alone works on second day, again P and Q on third day and so on, on alternate days till the work completed. Q and R together can complete the work in 10 days and efficiency of Q is twice the efficiency of R. Number of days taken by P to complete the work is five more than that of Q. Find the number of days in which the work will be completed?
a) 9(3/7) days
b) 10(4/7) days
c) 11(5/7) days
d) 12(6/7) days
e) 13 days
2) The perimeter of a rectangular field is thrice the perimeter of a square field. If one of the sides of the square field is 24 m and breadth of the rectangular field is 48 m then find the area of the rectangular field?
a) 4276 Sq m
b) 5354 Sq m
c) 3892 Sq m
d) 4608 Sq m
e) None of these
3) If 33 men can do a piece of work in 15 days by working for 8 hours then find in how many days 44 men can do the same work by working 6 hours a day?Â
a) 15 days
b) 18 days
c) 20 days
d) 12 days
e) None of these
4) The difference between simple interest and compound interest on Rs. 35000 at the rate of 12 % per annum for 2 years is?
a) Rs. 782
b) Rs. 504
c) Rs. 656
d) Rs. 958
e) None of these
5) Incomes of Rajesh and Mani are in the ratio 8: 9 and their expenditures are in the ratio of 33: 37. If Rajesh saves Rs. 14000 and Mani saves Rs. 16000, then find the income of Rajesh?
a) Rs. 35000
b) Rs. 50000
c) Rs. 80000
d) Rs. 60000
e) None of these
6) A man takes to row 120 km along the stream is one-third of the time taken to row against the stream. Find the speed of the boat in still water if the speed of stream is 8 km/hr?
a) 18 km/hr
b) 20 km/hr
c) 16 km/hr
d) 14 km/hr
e) None of these
7) An article was sold at a discount of 25 % and there was a profit of 20 %. If the profit earned was Rs. 100 less than the discount offered, then find the selling price of the article?
a) Rs. 650
b) Rs. 700
c) Rs. 750
d) Rs. 600
e) None of these
8) A basket contains 7 White, 5 Black, 2 Pink and 4 Green balls. If three balls picked up random, then find the probability that all three are Green balls?
a) 1/204
b) 15/157
c) 37/218
d) 23/512
e) None of these
9) 5 years ago, the ages of Agila and Hema are in the ratio of 3: 2. Three years ago, Agila’s age is equal to Hema’s age after 2 years. Then find the present age Agila?
a) 18 years
b) 24 years
c) 26 years
d) 20 years
e) None of these
10) A, B and C entered into a partnership with investment of Rs. 24000, Rs. 32000 and Rs. 48000 respectively. After one year A withdrew Rs. 4000 and B invested Rs. 8000 more. And after one more year A invested Rs. 15000 more and C withdrew Rs. 8000. At the end of three years, they earned a profit of Rs. 114450. Find the share of A in the total profit?
a) Rs. 33500
b) Rs. 30250
c) Rs. 27650
d) Rs. 35750
e) None of these
Answers :
1) Answer: d)
1/Q = 2/R ——— (i)
1/Q + 1/R = 1/10 ———— (ii)
From (i) and (ii),
=> 2/R + 1/R = 1/10
=> 3/R = 1/10
=> 1/R = 1/30
From (i)
1/Q = 2/30
=> 1/Q = 1/15
And
1/P = 1/20
Part of the work completed in 2 days = (1/20 + 1/15) + 1/30 = (3 + 4 + 2)/60 = 9/60 = 3/20
Part of the work completed in (2 x 6 = 12 days) = 3/20 x 6 = 18/20
Remaining work = 1 – 18/20 = (20 – 18)/20 = 2/20 = 1/10
Let, time taken by P and Q to complete remaining part of the work = n days
n x (1/20 + 1/15) = 1/10
=> n x (3 + 4)/60 = 1/10
=> n = 60/7 x 1/10
=> n = 6/7 days
Required number of days = 12 + 6/7 = 12(6/7) days
(Or)
LCM of 20, 15 and 30 = 60
Total work = 60 units
P = 60/20 = 3 units per day
Q = 60/15 = 4 units per day
R = 60/30 = 2 units per day
Work completed in 2 days = 3 + 4 + 2 = 9 units
Part of the work completed in (2 x 6 = 12 days) = 9 * 6 = 54 units
Remaining = 60 – 54 = 6 units
Remaining work completed by P and Q = 6/7
Total number of days = 12 + 6/7 = 12 (6/7) days
2) Answer: d)
Perimeter of square field= 24 * 4 = 96 m
Perimeter of the rectangular field= 96 * 3 = 288 m
Let the length of the rectangular field be x,
288 = 2 * (x+48)
288 – 96 = 2x
x = 96 m
Area of the rectangular field = 96 * 48 = 4608 Sq. m
3) Answer: a)
Let the number of days required be x,
M1 * D1 * H1 = M2 * D2 * H2
33 * 15 * 8= 44 * 6 * x
x = (33 * 15 * 8) / (44 * 6)
x = 15 days
4) Answer: b)
The difference between simple interest and compound interest on certain time for 2 years is,
= > Diff = Sum * (r/100)2
= > Diff = 35000 * (12/100)2
= > Diff = 35000 * (3/25)2
= > Diff = 35000 * (9/625) = Rs. 504
5) Answer: c)
Incomes and Rajesh and Mani are in the ratio = 8 : 9 (8x, 9x)
According to the question,
(8x – 14000) / (9x – 16000) = 33/37
= > 296x – 518000 = 297x – 528000
= > 10000 = x
Income of Rajesh = Rs. 80000
6) Answer: c)
Let us take the speed of the boat in still water be x km/hr,
120 / (x+8) = (1/3) * (120 / (x – 8))
3x – 24 = x + 8
2x = 32
x = 16
Speed of the boat in still water = 16 km/hr
7) Answer: d)
Let the cost price be x,
Selling price = (120/100) * x = 6x/5
Marked price * (75/100) = 6x/5
MP = 8x/5
The profit earned was Rs. 100 less than the discount,
According to the question,
= > (8x/5 – 6x/5) – (6x/5 – x) = 100
= > 2x/5 – x/5 = 100
= > x/5 = 100
Cost price = Rs. 500
Selling price = 500 * (120/100) = Rs. 600
8) Answer: a)
Total Balls = 18
Required Probability = 4C3 / 18C3 = 1/204
9) Answer: d)
5 years ago, Agila: Hema = 3: 2 (3x, 2x)
Present ages of Agila and Hema = 3x + 5, 2x + 5
Three years ago, Agila’s age is equal to Hema’s age after 2 years,
= > 3x + 2 = 2x + 7
= > x = 5
Present age of Agila = 3x + 5 = 20 years
10) Answer: c)
The share of A, B and C,
= > (24000 * 1 + 20000 * 1 + 35000 * 1): (32000 * 1 + 40000 * 2): (48000 * 2 + 40000 * 1)
= > 79000 : 112000 : 136000
= > 79 : 112 : 136
Total profit = Rs. 114450
327’s = 114450
1’s = 350
The share of A = 79’s = Rs. 27650
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