Question: 1 -
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
-
44, 36
-
42, 36
-
44, 33
-
42, 33
Answer:
42, 33
Solution:
Let the marks secured by them be x and (x+9)
sum of their marks =x+(x+9)=2x+9
Given that (x+9) was 56% of the sum of their marks.
⇒(x+9)=(56/100)(2x+9)⇒(x+9)=(14/25)(2x+9)⇒25x+225=28x+126⇒3x=99⇒x=33
Then (x+9)=33+9=42
Hence their marks are 33 and 42
Let the marks secured by them be x and (x+9)
sum of their marks =x+(x+9)=2x+9
Given that (x+9) was 56% of the sum of their marks.
⇒(x+9)=(56/100)(2x+9)⇒(x+9)=(14/25)(2x+9)⇒25x+225=28x+126⇒3x=99⇒x=33
Then (x+9)=33+9=42
Hence their marks are 33 and 42
Question: 2 -
Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
-
1:2
-
1:1
-
2:1
-
4:3
Answer:
4:3
Solution:
5% of A + 4% of B =(2/3)(6% of A + 8% of B)
=> (5A/100)+(4B/100)=(2/3)(6A100+8B100)
=> 5A + 4B =(2/3)(6A+ 8B)
=> 15A + 12B = 12A+ 16B
=> 3A = 4B
=> A : B = 4 : 3
5% of A + 4% of B =(2/3)(6% of A + 8% of B)
=> (5A/100)+(4B/100)=(2/3)(6A100+8B100)
=> 5A + 4B =(2/3)(6A+ 8B)
=> 15A + 12B = 12A+ 16B
=> 3A = 4B
=> A : B = 4 : 3
Question: 3 -
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
-
Rs. 250
-
Rs. 150
-
Rs. 300
-
Rs. 200
Answer:
Rs. 250
Solution:
amount paid to X per week =x and the amount paid to Y per week =y
Then x+y=550 ⋯(1)
But x=120% of y =120y/100=12y/10 ⋯(2)
From (1) and (2)
(12y/10)+y=550⇒22y/10=550⇒y=5500/22=500/2=250
amount paid to X per week =x and the amount paid to Y per week =y
Then x+y=550 ⋯(1)
But x=120% of y =120y/100=12y/10 ⋯(2)
From (1) and (2)
(12y/10)+y=550⇒22y/10=550⇒y=5500/22=500/2=250
Question: 4 -
The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year?
-
6%
-
4%
-
50%
-
5%
Answer:
5%
Solution:
increase in the population in 10 years
=262500−175000=87500
percent increase in the population in 10 years
=(87500/175000)×100=8750/175=50%
average percent increase of population per year
=50%/10=5%
increase in the population in 10 years
=262500−175000=87500
percent increase in the population in 10 years
=(87500/175000)×100=8750/175=50%
average percent increase of population per year
=50%/10=5%
Question: 5 -
Rahul went to a shop and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
-
Rs. 16.80
-
Rs. 12.10
-
Rs. 15
-
Rs. 19.70
Answer:
Rs. 19.70
Solution:
tax = 30 paise = Rs.0.3
tax is 6%.
i.e., Rs.0.3 is 6% of the taxable item.
Therefore, cost of taxable item =(0.3×100)/6=5
cost of the tax free items =25−(0.3+5)=19.7
tax = 30 paise = Rs.0.3
tax is 6%.
i.e., Rs.0.3 is 6% of the taxable item.
Therefore, cost of taxable item =(0.3×100)/6=5
cost of the tax free items =25−(0.3+5)=19.7