Aptitude Questions - 2
1.
Two
boats are sailing in the sea on the two sides of a light house. The height of
the light house is 100 meters. The angle of elevation to the top of the light
house was observed by one boat as 30° and by the other boat as 45°. What is the
distance between the two boats?
Answer: 273 meters.
A Let B and D be the two
Boats
and AC the Light
house.
The height of AC
is 100 meters. Angle
ABC
is 30° and Angle
B C D ADC is 45°
Now
we have two information, namely Sine angle ABC
= 30° = 100 / x = 1 / 2. (where x
is the length of AB) Hence x = 200.
AB^2
= AC62 + BC^2 200^2 = 100^2 +
x^2 x^2 = 200^2 – 100^2 = 30,000
X
= √30,000 = 173.20 meters.
Similarly,
Sine ADC = 45° = 100 / y = 1 / √2 Hence
y = 100 x √2 (where y is the
length AD.
Now, we have
y^2 = 100^2 x 2 = 20000
Thus
AD^2 = AC^2 + CD^2 ie 20000 = 10000 + CD^2. CD^2 =
10000
CD
= 100
Hence the distance between the two
boats ie B and D is 173.20 + 100 = 273.20 meters or say 273 meters.
2.
A
businessman has fixed the selling price of his goods at 30% over his cost
price. He sells half of his goods at this price. One quarter of his goods he
sells at a discount of 15% to this selling price and the remaining he sells at
a discount of 30% to the selling price.
What is his percentage gain or loss in the transaction?
Answer: Gain 15.375%
Let
us assume the trader had 100 articles purchased at a cost of Rs 100 each.
His
total cost price is 100 * 100 = 10,000
50
of these he sells at Rs 130.00 Amount realised Rs 6500.00
25
of these he sells at Rs 110.50
(after
allowing discount of 15%)
Amount realised Rs
2762.50
Remaining
25 he sells at Rs 91.00
After
allowing discount of 30%
Amount realised Rs 2275.00
Total
realization Rs
11537.50
Total
cost of purchase Rs
10000.00
Net
gain Rs 1537.50
Percentage of gain 15.375%
3.
A
train moves 50% faster than a car. Both starts from a place X at the same time
and reach place Y, 75 km away at the same time. The train however loses 15
minutes due to stoppages at stations en-route. What is the speed of the car?
Answer: 100 kmph.
Let
x be the speed of the car. Then time taken by the car to reach Y is 75 / x.
The
speed of the train is 3x/2. The time
taken by the train to reach Y is (75 / 3x/2) – ¼ hour.
So
we have an equation 75/x – 150/3x = ¼ Solving,
we get x = 100 kmph.
4.
In
a 50 over cricket match the run rate in the first 15 overs was only 4.2. What
should be the run rate in the remaining overs to reach the target of 298 runs?
Answer: 6.7
Total
runs in the first 15 overs 4.2 *
15 = 63
Remaining
runs to reach the target 235
Remaining
overs to achieve the target 35
Required run rate is 235 / 35
= 6.71 or say 6.7
5.
Atal
bought an article and spent Rs 110 on its repair and sold the same to Behari at
a profit of 20%. Behari sold it to Chauhan at a loss of 10%. Chauhan finally
sold the article for Rs 1188 making a profit of 10% in the deal. At what price
did Atal purchase the article?
Answer: Rs 890
For
Chauhan: If the cost price was 100 with
the profit of 10% the sale price was 110%. He sold the article for Rs 1188.
Hence
Chauhan’s purchase price was 1188 *
100/110 = 1080.
For Behari: He sold the article for 10% loss.
His sale price is Chauhan’s purchase price ie 1080.
Hence,
Behari’s purchase price was 1080 * 100 / 90 = 1200
For
Atal: He sold the article for 20% profit. Behari’s purchase price is Atal’s
Sale price ie 1200.
Atal’
purchase price inclusive of repair charges was 1200 * 100 / 120 = 1000
Excluding the repair charges of 110,
the purchase price of the article for Atal was Rs 890.00
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