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Question 1 of 5
1. Question
What is the sum of all natural numbers between 100 and 200 which are multiples of 3?
Correct
Solution: A) 4950
Multiples of 3 between 100 and 200 are 102, 105, 108,.. 198.
Here, the first term = 102
last term = 198
Let the number of Multiples of 3 between 100 and 200 = nArithmetic Progression Formula:
an = a1 + (n – 1)d
Where, an = last term = 198
a1 = first term = 102
d = common difference = 105 – 102 = 3
—> 198 = 102 + (n – 1) * 3
—> 198 – 102 = (n – 1) * 3
—> 96 = (n – 1) * 3
—> (n – 1) = 96/3 = 32
—> n = 32 + 1
—> n = 33Formula:
Sum of n terms = Sn = (n/2) * (a1 + an )
where n = number of elements = 33
a1 = first term = 102
an= last term = 198
Thus, using the above formula, Sum of all natural numbers between 100 and 200 which are multiples of 3 = (33/2) * (102 + 198)
= (33/2) * 300
= 33 * 150
= 4950Incorrect
Solution: A) 4950
Multiples of 3 between 100 and 200 are 102, 105, 108,.. 198.
Here, the first term = 102
last term = 198
Let the number of Multiples of 3 between 100 and 200 = nArithmetic Progression Formula:
an = a1 + (n – 1)d
Where, an = last term = 198
a1 = first term = 102
d = common difference = 105 – 102 = 3
—> 198 = 102 + (n – 1) * 3
—> 198 – 102 = (n – 1) * 3
—> 96 = (n – 1) * 3
—> (n – 1) = 96/3 = 32
—> n = 32 + 1
—> n = 33Formula:
Sum of n terms = Sn = (n/2) * (a1 + an )
where n = number of elements = 33
a1 = first term = 102
an= last term = 198
Thus, using the above formula, Sum of all natural numbers between 100 and 200 which are multiples of 3 = (33/2) * (102 + 198)
= (33/2) * 300
= 33 * 150
= 4950 -
Question 2 of 5
2. Question
Ramya invested an amount of Rs.60000 to start a business . After 8 months, Bharathi joined her with an amount of Rs . 30000 . They earned profit RS . 24500 after one year. What is Bharathi profit ?
Correct
Solution: C) 3500
Ratio of capital invested by each partner.
i.e Ramya and Bharathi for one year in order to get same profit.Ramya invested for 12 months whereas Bharathi invested for 4 months. Therefore,
= 12 * 60000 : 4 * 30000
= 720000 : 120000
= 6 : 1
Share of Bharathi out of Rs .24500
= 1/7 * 24500
= Rs. 3500Incorrect
Solution: C) 3500
Ratio of capital invested by each partner.
i.e Ramya and Bharathi for one year in order to get same profit.Ramya invested for 12 months whereas Bharathi invested for 4 months. Therefore,
= 12 * 60000 : 4 * 30000
= 720000 : 120000
= 6 : 1
Share of Bharathi out of Rs .24500
= 1/7 * 24500
= Rs. 3500 -
Question 3 of 5
3. Question
Dheeraj sold an article for Rs. 6,750 after giving a discount of 10% on the labelled price. He would have earned a profit of 50%, had there been no discount. What was the actual percentage of profit earned?
Correct
Solution: C) 35%
Let the marked price of the article be Rs. xDiscount = 10%
Then, the selling price = – 10% of = (9x/10)
Now,= (9x/10)= 6750 Or x = Rs. 7,500
As per the question, if the selling price is Rs. 7,500, then the profit earned by the Dheeraj is 50%.
So, the cost price = Rs. 5,000
Therefore, the actual percentage of profit earned by selling the article for Rs. 6,750 = (Profit/CP) × 100 =(1750/5000)× 100 = 35%
Hence, option (c) is the correct.Incorrect
Solution: C) 35%
Let the marked price of the article be Rs. xDiscount = 10%
Then, the selling price = – 10% of = (9x/10)
Now,= (9x/10)= 6750 Or x = Rs. 7,500
As per the question, if the selling price is Rs. 7,500, then the profit earned by the Dheeraj is 50%.
So, the cost price = Rs. 5,000
Therefore, the actual percentage of profit earned by selling the article for Rs. 6,750 = (Profit/CP) × 100 =(1750/5000)× 100 = 35%
Hence, option (c) is the correct. -
Question 4 of 5
4. Question
The length of a rectangle is decreased by 20% and breadth increased by 20%. What will be the net percentage increase/decrease in the area of the rectangle?
Correct
Solution: D) Decrease by 4%
Let the original length of the rectangle is x units
Let the original length of the rectangle be y units.
Thus, original area of rectangle = xy units^2 .
If the length of a rectangle is decreased by 20%, then new length will be 0.8 x units.
If breadth of rectangle is increased by 20%, then new breadth will be 1.2 y units.
Area of new rectangle will be 0.8x * 1.2y units^2
- Area of new rectangle will be = 0.96 xy units^2
Hence, Area of new rectangle will be 4 % less than the area of original rectangle.
Hence, option (d) is correct.
Incorrect
Solution: D) Decrease by 4%
Let the original length of the rectangle is x units
Let the original length of the rectangle be y units.
Thus, original area of rectangle = xy units^2 .
If the length of a rectangle is decreased by 20%, then new length will be 0.8 x units.
If breadth of rectangle is increased by 20%, then new breadth will be 1.2 y units.
Area of new rectangle will be 0.8x * 1.2y units^2
- Area of new rectangle will be = 0.96 xy units^2
Hence, Area of new rectangle will be 4 % less than the area of original rectangle.
Hence, option (d) is correct.
-
Question 5 of 5
5. Question
A tap can fill a water tank in 8 minutes. After one fourth of the tank is filled, two more taps with same capacity are opened. What is the total time taken to fill the tank completely?
Correct
Solution: B) 4 minutes
Since 1 part is filled in 8 minutes.
Therefore, 1/4 part is filled in 8×1/4 = 2 minutes.
Remaining part = 1 – ¼ = 3/4.
Since 1 part is filled in 8 minute, therefore, in 1 minute 1/8 part is filled.
Hence, in 1 minute, part filled by 3 (=1+2) taps = 3/8.Since 3/8 part is filled in 1 minute.
Therefore, 1 part is filled in 1/(3/8) = 8/3 minutes.
Therefore, 3/4 part is filled in (8/3)×(3/4) = 2 minutes.
So, the total time taken = 2 + 2 = 4 minutes.Hence, option (b) is correct.
Incorrect
Solution: B) 4 minutes
Since 1 part is filled in 8 minutes.
Therefore, 1/4 part is filled in 8×1/4 = 2 minutes.
Remaining part = 1 – ¼ = 3/4.
Since 1 part is filled in 8 minute, therefore, in 1 minute 1/8 part is filled.
Hence, in 1 minute, part filled by 3 (=1+2) taps = 3/8.Since 3/8 part is filled in 1 minute.
Therefore, 1 part is filled in 1/(3/8) = 8/3 minutes.
Therefore, 3/4 part is filled in (8/3)×(3/4) = 2 minutes.
So, the total time taken = 2 + 2 = 4 minutes.Hence, option (b) is correct.
