Q1. The vehicle of Mr. Ghosh needs 30% more fuel at the speed of 75 kmph than it needs at the speed of 50 kmph. At a speed of 50 kmph, Mr. Ghosh can go to a distance of 195 kms. At the speed of 75 kmph, what distance he will travel?

A 125 km
B 150 km
C 140 km
D 175 km
E 200 km

Q2. A starts a company and after 3 months B also joins the company. The initial investment of A and B is in the ratio of 3:2, respectively. A and B receives Rs. (x + 600) and Rs. (x – 360), respectively as profit after completion of one year of the company. Find the profit Share of B.

A Rs. 960
B Rs. 1320
C Rs. 1920
D Rs. 2460

E None

Q3. On the occasion of Raksha-Bandhan, there are (x + 10) boys and (x + 6) girls in a community hall, each girl tied the rakhi on the wrist of every boy, and every boy gave a chocolate to each girl as return gift, if total number of rakhi and chocolates used was 1344, then find the value of x?

A 12
B 15
C 18
D 24

E 28

Q4. Two numbers are in the ratio of 8:x, respectively. If 14 is added to the first number and 6 is subtracted from second number then ratio becomes 5:3, respectively. Find the value of x, if the difference between two numbers is 24. (Note: 8? x)

A 3
B 4
C 5
D 6
E 7

Q5. The average salary of all the employees in a bank is Rs. 800 per day. The average salary of clerks and managers is Rs.500 per day and Rs. 1250 per day, respectively. Find the number of clerks if there are total 20 employees in the branch. (Employees = Clerks + Managers)

A 4
B 8
C 12
D 16
E None

Q6.The profit earned on selling an article for Rs. (x + 200) is twice the loss incurred on selling the same article for Rs. (x – 250). Find the value of ‘x’, if to earn a profit of 20%, it must be sell for Rs. 1140.

A 750
B 850
C 950
D 1050
E 1150

Q7. The sum of perimeter of a rectangle(R) and a square(S) is 210 cm. The length and breadth of rectangle(R) is 40% more and 20% less than the side of square(S), what is the length of diagonal of rectangle(R)?

A 40√5 cm
B 5√65 cm
C 4√35 cm
D 25√2 cm
E 16√30 cm

Q8. A bag contains 36 balls of 3 different colors Magenta, Khaki, and Violet. The probability of drawing a Khaki ball is 1/4, and the ratio of number of Magenta balls to the number of Violet ball is 5:4. If 2 balls are drawn from the bag randomly then what will be the probability that two balls are of same color?

A 23/70
B 1/12
C 11/105
D 2/35
E None of these

Q9. Sita and Gita together can complete a work in 18 days. Sita starts the work and completes one-third of work in ‘x’ days and leaves the work. The remaining work is done by Gita in ‘x’ days. Find the time taken by Rita to complete the same work who is 20% more efficient than Sita.

A 18 days
B 24 days
C 36 days
D 45 days
E 54 days

Q10. Ram and Shyam invested in a scheme offering simple interest for same period of time. If interest obtained by Ram and Shyam at rate of 8% per annum and 12% per annum, respectively is Rs. 2232 and Rs. 2700, respectively. Find the amount invested by Shyam if amount invested by Ram is Rs. 1800 more than amount invested by Shyam.

A Rs. 7500
B Rs. 8000
C Rs. 8500
D Rs. 9000
E Rs. 9500

Solution:

Q1. SOL: B

The only thing which matters in this problem is mileage or kms per litre of the fuel. At 50 kmph, 195 kms can be covered.
According to given condition, 1.3 times the fuel will be required at 75 kmph.

Hence, distance traveled will be 195/1.3 = 150 kms

Q2.
SOL: A

The ratio of profit share of A and B is
A: B = 3 × 12: 2 × (12 – 3) = 2: 1
According to question,
(x + 600)/(x – 360) = 2: 1
x + 600 = 2x – 720
3x – 2x = 600 + 720
x = 1320
Therefore, profit share of B = 1320 – 360 = Rs. 960

Q3. SOL:  C

Number of rakhi used = (x + 10)(x + 6)
Number of chocolates used= (x + 6)(x + 10)
According to question,
(x + 10)(x + 6) + (x + 6)(x + 10) = 1344
x + 16x + 60 + x + 16x + 60 = 1344
x + 16x + 60 = 672
x + 16x – 612 = 0
x + 34x – 18x – 612 = 0
x(x+ 34) – 18(x + 34) = 0
(x + 34)(x – 18) = 0
x = -34 or x = 18

Q4.  SOL: D

Let, the two numbers be 8k and kx.
According to question,
8k – kx = 24
k(8 – x) = 24… (i)
And, (8k + 14): (kx – 6) = 5: 3
24k + 42 = 5kx – 30
k(24 – 5x) = -72
k(5x – 24) = 72
Using, equation (i), we get,
(24/(8 – x)) × (5x – 24) = 72
120x – 576 = 576 – 72x
120x + 72x = 1152
192x = 1152
x = 1152 ÷ 192 = 6

Q5.  SOL:  C

Let, the number of clerk be ‘x’
So, number of managers be (20 – x).
According to question,
(20 – x) × 1250 + x × 500 = 800 × 20
25000 – 1250x + 500x = 16000
750x = 25000 – 16000
750x = 9000
x = 9000 ÷ 750
x = 12

Q6. SOL: D

Cost price of article = 1140 ÷ 1.2 = Rs. 950
According to question,
(x + 200) – 950 = 2(950 – (x – 250))
x – 750 = 2(950 – x + 250)
x = 2400 – 2x + 750
3x = 3150
x = 3150 ÷ 3
x = 1050

Q7. SOL: B

Let, the side of square be ‘s’ cm.
So, length of rectangle = 1.4s cm
And, breadth of rectangle = 0.8s cm
According to question,
2(1.4s + 0.8s) + 4s = 210
4.4s+ 4s = 210
8.4s= 210
s = 210 ÷ 8.4
s = 25 cm
So, length of rectangle = 1.4 × 25 = 35 cm
And breadth of rectangle = 0.8 × 25 = 20 cm
So, diagonal of rectangle = √(35) + (20) = √1625 = 5√65 cm

Q8. SOL: A

Probability of drawing a Khaki ball = 1/4,
So, number of Khaki balls = (1/4) × 36 = 9
Therefore, number of balls of Magenta and Violet colours = 36 – 9 = 27
So, number of Magenta balls = (5/9) × 27 = 15
And, number of Violet balls = 27 – 15 = 12
Therefore, required probability = ( C + C + C )/ C = (9 × 4 + 15 × 7 + 6 ×
11)/(18 × 35) = 23/70

Q9. SOL: D

Time taken by Sita to complete the work = 3x days
Time taken by Gita to complete the work = (3/2)x days
According to question,
1/3x + 2/3x = 1/18
3/3x = 1/18
x = 18
So, time taken by Sita to complete the work = 54 days
Therefore, time taken by Rita to complete the work = 54/1.2 = 45 days.
Q10. SOL: A

Let, amount invested by Shyam is Rs. S, and time of investment is ‘t’ years.
So, amount invested by Ram is Rs. (S + 1800).
According to question,
S × 12% × t = 2700
Also, (S + 1800) × 8% × t = 2232
From both equations, we get,
2700/12S = 2232/8(S + 1800)
225/S = 279/(S + 1800)
225S + 405000 = 279S
54S = 405000
S = 405000/54
S = 7500

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