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Inequality
Directions (1 – 5): Each question contains three quantities as Quantity I, quantity II and Quantity III. You have to determine the relationship between them and give answer as,
1) Quantity I: Nithya can do a job in 15 days alone and Priya can do the same job in 18 days alone. A third person Kalai whose efficiency is (5/11)th of efficiency of both Nithya and Priya together, can do the same job in how many days alone?
Quantity II: A and B together can do a piece of work in 120/11 days. If A and B receives Rs.600 and Rs.500 respectively, then find the number of days taken by B alone.
Quantity III: P and Q together can do a piece of work in 20/3 days. R and S together can do the same work in 10 days. Q and R together can do the same work in 6 days. Find the number of days taken by P alone to complete the work, if S alone can do the same work in 30 days.
Which of the following should be placed in the blank spaces of the expression “Quantity I__ Quantity II___Quantity III” from left to right with respect to the above statements?
a) >, <
b) <, >
c) >, =
d) >, ≥
e) ≤, ≥
2) Quantity I: Marked price of an article is 50% more than the cost price. If the shopkeeper gives discount of 10% and cost price of that article is Rs 100 and he sale his 40 articles, then find the profit earned by him.
Quantity II: Seeta bought an article at 10% discount on the marked price. Seeta marks 20% above and sells to Geeta at a discount of 20%. If Geeta pays Rs. 864, then find the marked price of an article.
Quantity III: A and B enter into a partnership with a capital ratio of 4: 5. After 3 months, A withdrew 3/4th and receives Rs.3500 from the total profit at the end of the year, then find the total profit.
Which of the following should be placed in the blank spaces of the expression “Quantity I__ Quantity II___Quantity III” from left to right with respect to the above statements?
a) >, <
b) =, <
c) >, =
d) >, ≥
e) ≤, ≥
3) Quantity I: 6 hrs
Quantity II: A man can covers 48 km distance in 4 hours. If he increases his speed by 20% then find the time taken to cross 72 km.
Quantity III: Pipe A, B and C together can fill a tank in 8 hrs, while C and A together can fill a tank in 12 hrs. If A is 33(1/3)% efficient of pipe C, then find the time taken by Pipe B and C together to the fill the tank?
Which of the following should be placed in the blank spaces of the expression “Quantity I__ Quantity II___Quantity III” from left to right with respect to the above statements?
a) >, <
b) =, <
c) >, =
d) >, ≥
e) ≤, ≥
4) Quantity I: There are 6 men and 6 women in a class, from these 4 members are to be selected to form a committee. Find the number of ways that at least two women were in the committee.
Quantity II: A and B together can do a piece of work in 6 (6/7) days with the help of C finishes in 5 (1/3) days. If C got Rs.200 as wage, then find the total wages of A, B and C.
Quantity III: A retailer purchases a sewing machine at discount of 15% and sells it for Rs.1955. In the bargain he makes a profit of 15%. How much is the discount which he got from the wholesale?
Which of the following should be placed in the blank spaces of the expression “Quantity I__ Quantity II___Quantity III” from left to right with respect to the above statements?
a) >, <
b) =, <
c) >, =
d) <, >
e) ≤, ≥
5) Quantity I: In a class 45 students boys and girls are in the ratio of 5: 4. The average age of boys is 36 years and a girl is 22.5 years. Find the average age of the class
Quantity II: The ages of Rahul and Praveen are 40 years and 60 years, respectively. How many years before the ratio of their ages was 3: 5?
Quantity III: The ages of Sam and Sudha are in the ratio of 4: 5. After 12 years the ratio of their ages will be 7: 8. What is the difference in their ages?
Which of the following should be placed in the blank spaces of the expression “Quantity I__ Quantity II___Quantity III” from left to right with respect to the above statements?
a) >, <
b) =, <
c) >, >
d) >, ≥
e) ≤, ≥
Data Interpretation
Directions (6 – 10): Study the following information carefully and answers the questions given below.
In the following table, the Investment and profit of three persons from different states is given.
Note: Some values are missing. You have to calculate these values as per data given in the questions.
6) Average Investment made by all of them in Chennai is Rs. 10,000 and average profit earned by all of them from the same city is Rs. 6000, then profit earned by R in the same city is what percent more/less than the amount invested by R in the same city?
a) 31 9/11 %
b) 23 ½ %
c) 33 1/5 %
d) 25 5/7 %
e) None of these
7) In Kolkata total Investment of P and Q is Rs. 85000, P and Q invested their amount for 4 months and 6 months respectively in the same city, then find the number of months that R invested his amount?
a) 8 months
b) 20 months
c) 16 months
d) 9 months
e) None of these
8) If P, Q and R invested in Surat city for 5 months, 8 months and 6 months respectively then profit earned by R from Surat city is what % of the profit earned by P and Q together from the same city,if total profit earned by all of them from Surat City is Rs. 8700?
a) 37%
b) 41%
c) 50%
d) 45%
e) None of these
9) If the total profit earned from Jaipur by all of them is Rs. 32375 and each invested for 9 months then find the ratio of investment of P in Jaipur city to the profit of Q from the Agra city?
a) 7: 15
b) 8: 7
c) 7: 16
d) 16: 19
e) None of these
10) If Person P invested his amount in Agra city for 9 months and person R invested his amount in the same city for 10 months then find the total profit made by all of them from Agra city?
a) Rs. 28750
b) Rs. 29750
c) Rs. 27725
d) Rs. 28250
e) None of these
Answers :
1) Answer: B
Quantity I:
According to the question,
One day work of Nithya and Priya together = (1/15) + (1/18)
= 11/90
Thus number of days taken by Kalai to complete the work = (90/11) * (11/5)
= 18 days
Quantity II:
Efficiency ratio of A and B = 600: 500 = 6: 5
Time ratio of A and B = 5: 6 = 5x : 6x
According to the question,
1/5x + 1/6x = 11/120
11/30x = 11/120
x = 4
Number of days taken by B alone = 6 * 4 = 24 days
Quantity III:
(P+ Q)’s one day work = 3/20
(Q+R)’s one day work = 1/6
(R+S)’s one day work = 1/10
R’s one day work = 1/10 – 1/30 = (3 – 1)/30 = 2/30 = 1/15
Q’s one day work = 1/6 – 1/15 = (5 – 2)/30 = 3/30 = 1/10
P’s one day work = 3/20 – 1/10 = (3 – 2)/20 = 1/20
P can complete the work in 20 days
Hence, Quantity I < Quantity II > Quantity III
2) Answer: A
Quantity I:
Let CP = 100
Then MP = 150
Now SP = (90/100) * 150
= 135
Thus profit percentage = 35%
Hence required amount = 100 * 40 * 35/100
= Rs.1400
Quantity II:
Let us take marked price of an article be Rs. X
According to the question,
x * 90/100 * 120/100 * 80/100 = 864
x = 864 * 100/90 * 100/120 * 100/80
x = Rs. 1000
Quantity III:
Profit ratio of A and B = (4x * 3+ 4x * 1/4 * 9): (5x * 12)
= (12x + 9x): 60x
= 21x: 60x
= 7: 20
Let us take the total profit be x
A’s share in the total profit = 3500
x * (7/27) = 3500
=> x = 500 * 27 = Rs.13500
Hence, Quantity I > Quantity II < Quantity III
3) Answer: A
Quantity I: 6 hrs
Quantity II:
Original speed = 48/4 = 12 km/hr
New speed = 12 * 120/100 = 14.4 km/hr
Required time = 72/14.4 = 5 hrs
Quantity III:
A + B + C = 8hrs
A + C = 12hrs
LCM of (8,12) = 24
Number of units of water filled by A, B and C together = 24/8 = 3 units
Number of units of water filled by A and C together = 24/12 = 2 units
(i.e.) Number of units of water filled by B = 3 – 2 = 1 units
Number of units of water filled by C in one hour = x units
Number of units of water filled by A in one hour = 33(1/3)% of x = x/3
A + C = 2 units
x + x/3 = 2
x = 1.5 units
Water filled by B and C together = 1 + 1.5 = 2.5 units
Time = 24/2.5 = 9.6 hrs
Hence, Quantity I < Quantity II > Quantity III
4) Answer: D
Quantity I:
Number of ways = (6C2 * 6C2) + (6C3 * 6C1) + (6C4)
= [(6 *5 /1 * 2) * (6 * 5/1(1 * 2)]+ [(6 * 5 * 4/1 * 2 * 3) * 6] + (6 * 5/1 * 2)
= (15 * 15) + (20 * 6) + 15
= 225 + 120 + 15
= 360
Quantity II:
C’s one day work = 3/16 – 7/48
= (9 – 7)/48
= 2/48
= 1/24
(A + B)’s one day work: C’s one day work = 7/48: 1/24
= 7: 2
C’s share = 2/9 of total wage = 200
Total wage = (200/2) * 9 = Rs.900
Quantity III:
Let the marked price be Rs. x
Discount = 15% of Rs. x
C.P. = (x – 15% of x) = Rs. 17x / 20
Then 15% of 17x / 20 = 1955 – 17x / 20
51x/400 + 17x/20 = 1955
x = 2000
Discount received by retailer = (15% of 2000) = Rs.300.
Hence, Quantity I < Quantity II > Quantity III
5) Answer: C
Quantity I:
According to the question,
45 * x = 25 * 36 + 20 * 22.5
45x = 900 + 450
x =1350/45 = 30 yrs
Quantity II:
Let x year ago, the ratio of Rahul and Praveen’s ages was 3: 5
(40 – x)/(60 – x) = 3/5
=> 200 – 5x = 180 – 3x
=> x = 10 years
Quantity III:
(4x + 12)/(5x + 12) = 7/8
32x + 96 = 35x + 84
3x = 12
x = 4
Difference in their ages = (5x – 4x) = x = 4 years
Hence, Quantity I > Quantity II > Quantity III
Directions (6-10) :
6) Answer: A
Average investment made by P, Q and R = 10000
Then total investment of P, Q and R = 10000 × 3 = Rs. 30000
Investment of P and Q in the Chennai is = Rs 9000 and Rs. 10000 respectively.
Then total investment of P and Q is = Rs. 9000 + 10000 = Rs. 19000
Then investment of R = 30000 – 19000 = Rs. 11000
Average profit made by P, Q and R = 6000
Then total profit of P, Q and R = 6000 × 3 = Rs. 18000
Profit of P and Q in the Chennai is = Rs 4500 and Rs. 6000 respectively.
Then total profit of P and Q is = Rs. 4500 + 6000 = Rs. 10500
Then profit of R = 18000 – 10500 = Rs. 7500
So, required profit percentage of R in Chennai
=> (11000 – 7500) / 11000 × 100
Solving we get = 31 9/11 %
7) Answer: B
In Kolkata total Investment of P and Q is Rs. 85000
Let investment of R is = Rs x
Then according to the question,
=>(x × 4) / (85000 – x)6 = 20000/30000
=>2x/3(85000 – x) = 2/3
=>6x=2×3×85000−6x
=>12x=6×85000
=> x =Rs. 42500
Investment of A = Rs. 42500
Investment of B= Rs. 42500
Let required months = y
Then (42500 × 6) / (17000 × y) = 30000/40000
Solving we get, y = 20 months
8) Answer: D
P invested Rs. 4000 for 5 months = 4000 × 5
Q invested Rs. 5000 for 8 months = 5000 × 8
R invested Rs. 4500 for 6 months = 4500 × 6
So, profit sharing ratio of P, Q and R will be
=> P : Q : R = (4000 × 5) : (5000 × 8) : (4500 × 6)
Solving we get = 20 : 40 : 27
Now, total profit earned by all of them in Surat city is Rs. 8700.
Then we can find the profit of P, Q and R
So, Profit of P = (20/87) × 8700 = Rs 2000
Profit of Q = (40/87) × 8700 = Rs. 4000
Profit of Re = (27/87) × 8700 = Rs. 2700.
So, required percentage profit of R = (2700/6000) × 100 = 45%
9) Answer: C
Investment of Q and R in the Jaipur city is Rs. 7000 and 8000 respectively.
So, (7000/8000) = Profit of Q / 14000
Solving we get, Profit of Q = Rs. 12250
Then profit of P = 32375 –12250 – 14000
So, profit of P = Rs. 6125
Let investment of P in Jaipur city = Rs. x
Then x/7000 = 6125/12250
Solving we get x = Rs. 3500
So, the required ratio will be = P: Q = 3500: 8000
Solving we get P: Q = 7: 16
10) Answer: E
P invested Rs. 15000 in Agra for 9 months = 15000 × 9
And R invested Rs. 20000 in Agra for 10 months = 20000 × 10
Profit of R in Agra is = Rs. 12500
Let Profit of P in Agra city is = Rs. x
Then according to the question,
=> (15000 × 9) / (20000 × 10) = x/12500
Solving we get = (27/50) = x/12500
=> x = Rs. 6750
So, required Profit will be = P + Q + R
=>Rs. 6750 + Rs. 8000 + Rs. 12500
=>Rs. 27250
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