81. In an examination out of 480 students, 85% of the girls and 70% of the boys have passed. How many boys appeared in the examination, if total pass percentage was 75%?
(a) 37
(b) 340
(c) 320
(d) 360
(e) None of these
Solution: (c)
Total number of students = 480
Percentage of total students passed
75% of total students =\(\displaystyle \frac{{75\times 480}}{{100}}=360\) students
Now, using the condition from the question,
Let the number of boys be x.
Then, 70% of x + 85% of (480 – x) = 360
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{75\times x}}{{100}}+\frac{{85\times (480-x}}{{100}}=360\)
\(\displaystyle \Rightarrow \)70x – 85x + 40800 = 36000
\(\displaystyle \Rightarrow \)40800 – 36000 = 85x – 70x
\(\displaystyle \Rightarrow \)x = \(\displaystyle \frac{{4800}}{{15}}=320\)
Therefore, there are 320 boys who appeared for the examination.
82. When the price of rice is increased by 25 percent, a family reduces its consumption such that the expenditure is only 10 percent more than before. If 40 kg of rice is consumed by family before, then find the new consumption of family.
(a) 35.2
(b) 35.2
(c) 36.2
(d) 37.2
(e) None of these
Solution: (b)
Suppose initialy price per kg of rice is 100 then their expenditure is 4000.
Now their expenditure is only increased by only 10% i.e – 4400.
Increased price of rice = 125.
So new consumption = \(\displaystyle \frac{{4400}}{{125}}=35.2\)
83. If 80% of A = 50% of B and B =x% of A, then the value of x is :
(a) 400
(b) 300
(c) 160
(d) 150
(e) 320
Solution: (c)
According to question,
\(\displaystyle A\times \frac{{80}}{{100}}=B\times \frac{{50}}{{100}}\)
Therefore, B=\(\displaystyle B=\frac{{A\times 80}}{{100}}1.6A\)
B = 160% of A
x = 160
84. If x is 80% of y, what percent of y is x ?
(a) 75%
(b) 80%
(c) 100%
(d) 125%
(e) 120%
Solution: (d)
According to question,
y= \(\displaystyle \frac{{100\times 100}}{{80}}\times x\)
y = 125% of x
85. If 15% of (A + B) = 25% of (A – B), then what per cent of B is equal to A?
(a) 10%
(b) 60%
(c) 200%
(d) 400%
(e) 450%
Solution: (d)
15% of (A + B)= 25% of (A – B)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{15}}{{100}}(A+B)=\frac{{25}}{{100}}(A-B)\)
\(\displaystyle \Rightarrow \)15 (A + B) = 25 (A – B)
\(\displaystyle \Rightarrow \)15 A + 15 B = 25A – 25 B
\(\displaystyle \Rightarrow \)10 A = 40 B
\(\displaystyle \Rightarrow \)A = 4 B
Now, let x% of B is equal to A
Therefore, \(\displaystyle \frac{X}{{100}}\times B=A\to \frac{X}{{100}}\times B=4B\)
x =400%
86. What is 20% of 25% of 300?
(a) 15
(b) 25
(c) 45
(d) 60
(e) 150
Solution: (a)
20% of 25% of 300
=\(\displaystyle \frac{{20}}{{100}}\times \frac{{25}}{{100}}\times 300\)
=\(\displaystyle \frac{1}{5}\times \frac{1}{4}\times 300=15\)
87. The time duration of 1 hour 45 minutes is what percent of a day?
89. Two numbers are respectively 20% and 50% of a third number. What per cent is the first number of the second?
(a) 10%
(b) 20%
(c) 30%
(d) 40%
(e) 50%
Solution: (d)
Let the third number be x,
According to the question;
First number = \(\displaystyle \frac{{20}}{{100}}\times x=\frac{x}{5}\)
Second number = \(\displaystyle \frac{{50}}{{100}}\times x=\frac{x}{2}\)
Therefore, required percentage = \(\displaystyle \frac{{\frac{x}{5}\times 100}}{{\frac{x}{2}}}=\frac{x}{5}\times \frac{2}{x}\times 100=40\%\)
90. Two numbers are respectively 25% and 20% less than a third number. What percent is the first number of the second ?
(a) 5%
(b) 75%
(c) 80%
(d) 93.75%
(e) 95%
Solution: (d)
If two numbers are respectively x% and y% less than the third number, first number as a percentage of second is \(\displaystyle \frac{{100-x}}{{100-y}}\times 100\%\)
Therefore, required percentage = \(\displaystyle \frac{{100-25}}{{100-20}}\times 100\%\)
=\(\displaystyle \frac{{75}}{{80}}\times 100\%=93.75\%\)
