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QUESTION: 1

If A = x% of y and B = y% of x, then which of the following is true?

Solution:

x%ofy=x/100×y

=y/100×x

=y%ofx

∴A=B

QUESTION: 2

Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

Solution:

QUESTION: 3

Two tailors 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?

Solution:

X+ y=Rs. 550

x = 120% of y

120% * y+ y =550

120/100*y+y = 550

6/5y+y =550

6y+5y/5 = 550

11/5y = 550

11y = 550*5

y = 250

QUESTION: 4

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

Solution:

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

QUESTION: 5

**Q. **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. The marks obtained by them are:

Solution:

QUESTION: 6

If 20% of a = b, then b% of 20 is the same as:

Solution:

20% of a = b => (20/100)a = b

b% of 20 =(b/100) x 20 = (20a/100) x (1/100) x (20) = 4a/100 = 4% of a.

QUESTION: 7

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.

Solution:

5100*A*+4100*B*=23[6*A*100+8*B*100]

5*A*+4*B*=2/3(6*A*+8*B*)

15*A*+12*B*=12*A*+16*B*

3*A*=4*B*

*A**/B*=4/3⇒

A : B = 4 : 3

QUESTION: 8

Gauri went to the stationers 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?

Solution:

Let the amout taxable purchases be Rs. x.

∴ Cost of tax free items = Rs. [25-(5+0.30)] = Rs. 19.70

QUESTION: 9

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

Solution:

Total Valid votes are = 80% of 7500= 6000

If one has 55% vote then the other has left with 45% votes

Hence, 45% of 6000= 2700

QUESTION: 10

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

Solution:

x-x(40/100)=420

x-40x/100=420

or, 60x/100=420

x=42000/60

x= 700

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