# Percentage 2

1. 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 : 3
(2) 1 : 1
(3) 3 : 4
(4) 4 : 3
(5) 2 : 1

Explanation :-
5% of A + 4% of B=2/3(6% of A+8% of B).
=>(5/100)×A+(4/100)×B = 2/3((6/100)×A+(8/100)×B).
=>(1/20)×A+(1/25)×B=(1/25)×A+(4/75)×B.
=>((1/20)−(1/25))×A=((4/75)−(1/25))×B.
=>(1/100)×A=(1/75)×B.
=>A/B=100/75=4/3.

2. 40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?
A.390
B.405
C.408
D.415

Explanation :-

(40/100)x390 + (60/100)x420 = 408

3. In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?
A.2
B.2.5
C.3
D.3.5

Explanation :-

Let the three numbers be x, y, and z. We are given that
(x+y)/2 =2
(y+z)/2 =3
(x+z)/2 =4
(x+y)/2+(y+z)/2+(x+z)/2 =2+3+4
x+y+z = 9
The average of the three numbers is,
(x+y+z)/3 = 9/3 = 3.

4. .A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
A.17
B.23
C.77
D.None of these

Explanation :-

let’s suppose the number of apples  be 100.
first day he sells 60% apples i.e.,60 apples.
Remaining apples =40.
He throws 15% of the remaining i.e., 15% of 40 = 6.
Now he has 406=34  apples
The next day he throws 50% of the remaining 34 apples i.e., 17.
In total he throws 17=6+17= 23 apples.