Percentage - Study Mode

[#241] A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Correct Answer

(B) $$45frac{5}{{11}}\% $$

Explanation

Solution: Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 110 - (60) = 50 ∴ Required percentage $$eqalign{
& = left( {frac{{50}}{{110}} imes 100}
ight)\% cr
& = 45frac{5}{{11}}\% cr} $$

[#242] 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:
Correct Answer

(C) 42, 33

Explanation

Solution: Let their marks be (x + 9) and x Then, $$eqalign{
& x + 9 = frac{{56}}{{100}}left( {x + 9 + x}
ight) cr
& Rightarrow 25left( {x + 9}
ight) = 14left( {2x + 9}
ight) cr
& Rightarrow 3x = 99 cr
& Rightarrow x = 33 cr} $$ So, their marks are 42 and 33

[#243] A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
Correct Answer

(D) 700 apples

Explanation

Solution: Suppose originally he had x apples Then, $$eqalign{
& left( {100 - 40}
ight)\% ,{ ext{of}},x = 420 cr
& Rightarrow frac{{60}}{{100}} imes x = 420 cr
& Rightarrow x = {frac{{420 imes 100}}{{60}}} = 700 cr} $$

[#244] What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Correct Answer

(C) 20%

Explanation

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 $$ = left( {frac{{14}}{{70}} imes 100}
ight)\% = 20\% $$

[#245] If A = x % of y and B = y % of x , then which of the following is true?
Correct Answer

A is smaller than B

Explanation

Solution: $$eqalign{
& x\% ,{ ext{of}},y = {frac{x}{{100}} imes y} cr
& ,,,,,,,,,,,,,,,,,,,, = {frac{y}{{100}} imes x} cr
& ,,,,,,,,,,,,,,,,,,,, = y\% ,{ ext{of}},x cr
& herefore A = B cr} $$