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Arithmetic : Level 3 Test -4

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Question 1
One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survive and remaining 50% die after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?
1 million
2 million
4 million
8 million
Question 1 Explanation: 
Let there be p bacteria in the first generation.
Hence, n1 = p.
Only p/2 among them will survive
Therefore (p/2)8 = 4p bacteria.
Now , n2 = 4p.
Only 2p will survive .
So in the third generation number of bacteria  = 8(2p) = 16p.
So n3 = 16p.so we have a pattern
n1 = p, n2 = 4p, n3 = 16p, n4 = 64p, this will form a GP with a = p and r = 4.
The seventh term of this GP = 4096.
So we can write 4096 = p(4)6
= p(2)12
= 4096p.
Hence, p = 1, i.e. 1 million.
Question 2
In a survey of political preferences, 78% of those asked were in favor of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?
Question 2 Explanation: 
Let p, q, r be the percentage of persons who is in favor of I and ii, I and iii , ii and iii
Also given that 5% is favored for all
So according to the question we have the equation
45 – (p +q) + 25 – (p + r) + 15 – (q + r) + (p + q + r + 5) = 78 ( p + q + r + 5 ) = 12
Therefore % who is in favor of more than one = 12 + 5 = 17
Question 3
Forty per cent of the employees of a certain company are men, and 75% of the men earn more than Rs. 25,000 per year. If 45% of the company’s employees earn more than Rs. 25,000 per year, what Fraction of the women employed by the company earn less than or equal to Rs. 25,000 per year?
Question 3 Explanation: 
Let there be 100 workers
So 40 will be men
60 will be women
Out of 40 men, 75% earn more than
i.e. 30 men earn more than Rs. 25,000.
If 45 people in the company earn more than 25000 then
that men 15 women out of 60 earn more than Rs. 25000.
Then women left that earn less than Rs. 25000 are 45 which is ¾ of 60
Question 4
A dealer buys dry fruits at Rs. 100, Rs. 80 and Rs. 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight, and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit (considering the selling price of each kind of dry fruit is equal)?
Rs. 80
Rs. 100
Rs. 95
None of these
Question 4 Explanation: 
Let him mix 3 kg, 4 kg and 5 kg of dry fruits
Therefore the cost will be = (3 x 100 + 4 x 80 + 5 x 60) = 920
Now he sell at 50% profit
Therefore selling price of 12 kg =1380
So the selling price of 1 kg = 1380/12 = Rs. 115
Question 5
Instead of a meter scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?
Question 5 Explanation: 
Let the price of 100 cm of cloth = Rs. 100 He got 120 cm in Rs. 100 Profit earned by him = 20 cm of cloth i.e. Rs. 20 Therefore the cost price of 1 cm for him was = Rs. 0.833
Now he sells 80 cm at Rs. 100
He now gives the discount of 20% on cash payment
Therefore by all transaction he gives 80 cm at Rs. 80
Therefore he only earns 20% profit by all transaction
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