1.If Suresh sells 7 star chocolate at 75% profit to Ramesh and Ramesh sells it to Mahesh at 20% loss. If Mahesh had to pay rupees 9. Find the original price.

Ans:2
Let original price be 100
So 75% profit
Price becomes 100 + 75 = 175
Ramesh sells it at 20% loss
So (20/100) x 175 = 35
So Mahesh buys it at 140
If Mahesh bought it at Rs. 140
So original price = 100
If Mahesh bought it at Rs. 9
By unitary method
X = (100 x 9) / 140
X = 6.42

 

2. Andre ‘Dre’ Johnson invests 12% of his monthly salary i.e., ₹2088 in Mutual Funds. His other investments are 16% of his salary in PPF and another 5% of his monthly salary in Insurance Policies. What is his total monthly investment?

Ans:4
Given, 12% of his monthly salary = ₹2088
=> His monthly salary = 2088/0.12 = ₹17400
He invests (12 + 16 + 5) = 33% of his monthly salary.
∴ His total investment = 0.33 * 17400 = ₹5742

 

3. A box contains eight red and ten blue balloons. Two draws of one balloon each are made without replacement. What is the probability that one balloon is red and the other balloon is blue?

Ans:1
Two balls can be drawn from 18 balloons in 18C2 Ways, i.e. 153 ways.
One red from 8 red balloon can be drawn in 8C1 = 8 ways
One blue balloon from 10 blue can be drawn in 10C1 = 10 ways.
∴ n(S) = 153, n(E) = 8 X 10 = 80
∴ P(E) = n(S) / n(E) = 80/153

 

4. Ratio of monthly income of three sisters Vatika, Mohita and Deepa is 9 : 5 : 7 and the ratio of their monthly saving is 5 : 3 : 8. If the highest income and highest saving of any of the sister is Rs 72000 and Rs 40000 respectively then what is the ratio of monthly expenditure of three sisters?

Ans:2
Ratio of monthly income of three sisters Vatika, Mohita and Deepa is 9 : 5 : 7 and it is also given that the highest income of any of the sister is Rs 72000.
From the given ratio we can see that income of Vatika is Rs 72000.
Hence Monthly income of Mohita and Deepa will be Rs 40000 and Rs 56000 respectively.
Now from the given ratio we can know that Deepa has the highest saving of Rs 40000.
So the savings of Vatika and Mohita will be Rs 25000 and Rs 15000 respectively.
Now monthly expenditure of Vatika = Rs (72000 – 25000) = Rs 47000
Monthly expenditure of Mohita= Rs (40000 – 15000) = Rs 25000 Monthly expenditure of Deepa = Rs (56000 – 40000) = Rs 16000
Therefore required ratio = 47000 : 25000 : 16000 = 47 : 25 : 16

 

5. Hans borrows Rs. 7000 at a simple interest from the village money lender. At the end of 3years, he again borrows Rs. 3000 and closes his account after paying Rs. 4615 as interest after 8 years from the time he made the first borrowing. Find the rate of interest.

Ans:4
Replace the solution with the following:
GivenIncorrec that, Hans borrowed Rs. 7000 at a simple interest
Let ‘r’ be the rate of interest
Simple interest paid for the first three years is (7000*3*r/100)
At the end of 3 years, he again borrows Rs. 3000
Simple interest paid for the next five years is (10000*5*r/100)
Hans paid Rs.4615 as simple interest at the end of 8 years
Now, (7000*3*r/100) + (10000*5*r/100) = 4615
210r + 500r = 4615
710r = 4615
r = 6.5

 

6. Two persons are walking in the same direction at speeds 4 km/hr and 8 km/hr. A train comes running from behind and passes them in 8 and 9 seconds respectively. The speed of the train is:

Ans:4
Let the speed of the train be S km/hour
Relative speed while crossing first person = (S-4) km/hour = (5/18)(S-4) m/s
Length of the train = (5/18) x (S-4) x 8
Relative speed while crossing second person = (S-8) km/hour = (5/18)(S-8) m/s
Length of the train = (5/18) x (S-8) x 9
Since Length is the same in both cases,
(5/18) x (S-4) x 8 = (5/18) x (S-8) x 9
8S – 32 = 9S – 72
S = 40 km/hr

 

7. Ajit and Sumit can complete a work together in 20 days, and Ajit alone can do the same work in 32 days. When both work together their efficiencies reduce by 20% compare to working alone. Find the number of days Sumit alone t

Ans:3
Let sumit take x days to complete the work.
Since the efficiency when they work together is 80% = 4/5,
we have (1/32) + (1/x) = (1/20) x (5/4)

 

8. A project can be completed by 2 men and 5 women in 8 days while 4 men and 6 women can complete the same in 5 days. How many men are required to complete the project in 4 days?

Ans:1
Let ‘a’ and ‘b’ be the amount of work done by each man and each woman respectively in a day.
8 x (2a + 5b) = 5 x (4a + 6b)
=> 4a = 10b
=> a = 2.5b
8 x (2a + 5b) = 1
=> 8 (2 x 2.5b + 5b) = 1
=> 80b = 1
=> b = 1/80
=> a = 1/32
So a man can complete the work in 32 days. Therefore, 8 men are required to complete the work in 4 days.

 

9. Two pipes A and B can fill a tank in 20 minutes and 15 minutes respectively. If both pipes are opened simultaneously, after how many minutes should pipe B be closed so that the tank is full in 12 minutes.

Ans:1
Suppose pipe B is closed after n minutes.
12/20 + n/15 = 1
=> n/15 = 2/5
=> n = 6
Hence option 1 is correct.

 

10. A shopkeeper buys notebooks at the rate of Rs. 45 each and earns a profit of 4%. He also buys pencil box at the rate of Rs. 80 each and earns a profit of 20%. How much profit will he earn in a day if he sells 10 notebooks and 6 pencil boxes?

Ans:5
Required profit = 45 x 0.04 x 10 + 80 x 0.2 x 6
= 18 + 96 = Rs 114

 

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