SSC > Simple and Decimal Fraction

Explanation

{tex} \frac{4}{7} = 0.57, \frac{5}{13} = 0.38, \frac{6}{11} = 0.54, \frac{3}{5} = 0.6, \frac{2}{3} = 0.67 {/tex}

So the second smallest fraction is {tex} \frac{6}{11} {/tex}

Explanation

1088.88 + 1800.08 + 1880.80 = 4769.76

Explanation

6435.9 + 7546.4 + 1203.5 = 15185.8

Explanation

726.34 + 888.12 - ? = 1001.88

Therefore, ? = 726.34 + 888.12 - 1001.88

= 1614.46 -1001.88 = 612.58

Explanation

{tex} \frac{16}{23} \times \frac{47}{288} \times \frac{92}{141} = \frac{4}{18 \times 3} = \frac{2}{9 \times 3} = \frac{2}{27} {/tex}

Explanation

{tex} 1\frac{3}{5}+1\frac{8}{9}+2\frac{4}{5} = \left(1+1+2\right) + \left(\frac{3}{5}+\frac{8}{9}+\frac{4}{5}\right) {/tex}

{tex} 4 + \frac{27+40+36}{45} {/tex}

{tex} 4 + \frac{103}{45} = 4 + 2\frac{13}{45} = 6\frac{13}{45} {/tex}

Explanation

{tex} \frac{19999}{21111} = 0.947 {/tex}

Explanation

{tex} ? = \frac{1212}{0.5 \times 6.06} = \frac{1212}{5 \times 606} \times 10 \times 100 {/tex}

= {tex} \frac{1212}{3030} \times 1000 = \frac{1212 \times 100}{303} = 400 {/tex}

Explanation

{tex} 33 + 371 \div 7 = 33 + \frac{371}{7} = 33 + 53 = 86 {/tex}

Explanation

{tex} \left(39.3 \times 53.4\right) + \left(26.7 \times 5.9\right) {/tex}

= {tex} 2098.62 + 157.53 = 2256.15{/tex}

Explanation

{tex} ? = \frac{3}{4} \times \frac{5}{6} \times \frac{7}{10} \times 1664 = 728 {/tex}

Explanation

{tex} \frac{19}{21} = 0.904, \frac{21}{25} = 0.84, \frac{25}{29} = 0.86 {/tex}

{tex} \frac{29}{31} = 0.93, \frac{31}{37} = 0.837 {/tex}

{tex} 0.837 < 0.84 < 0.86 < 0.904 < 0.93 {/tex}

{tex} Clearly, \ \frac{21}{25} \ will \ be \ on \ second \ number {/tex}

Explanation

{tex} ? = \frac{783}{9 \times 0.75} = 116 {/tex}

Explanation

4.00 + 4.44 + 44.40 + 4.04 + 444.00 = 500.88

Explanation

0.252525 = {tex} 0.\bar{25} = \frac{25}{99} {/tex}

Explanation

{tex} \frac{5}{7} = 0.71, \frac{4}{9} = 0.44, \frac{6}{11} = 0.54, \frac{2}{5} = 0.40, \frac{3}{4} = 0.75 {/tex}

Here, the largest fraction = {tex} \frac{3}{4} {/tex}

and the smallest fraction = {tex} \frac{2}{5} {/tex}

So, required difference = {tex} \frac{3}{4} - \frac{2}{5} = \frac{15 - 8}{20} = \frac{7}{20} {/tex}

Explanation

Let the original fraction be {tex} \frac{x}{y} {/tex}

Numerator is increased by 200%.

Therefore, Numerator = x + 200% of x

= {tex} x + \frac{200x}{100} {/tex}

= {tex} \frac{100x + 200x}{100} {/tex}

= {tex} \frac{300x}{100} {/tex}

and denominator of the fraction is by 150%.

Denominator = {tex} y + \frac{150y}{100} {/tex}

= {tex} \frac{100y + 15y}{100} {/tex}

= {tex} \frac{250y}{100} {/tex}

Then, according to the question,

{tex} \frac{300x/100}{250y/100} = \frac{9}{35} {/tex}

{tex} \frac{300x}{250y} = \frac{9}{35} {/tex}

Therefore, {tex} \frac{x}{y} = \frac{9}{35} \times \frac{250}{300} = \frac{3}{14} {/tex}

Explanation

Let A, B, C and D pay Rs.x, Rs.y, Rs.z andrs.a

According to the question,

{tex} x = \frac{1}{2} \left(y+z+a\right) {/tex} ...(i)

{tex} y = \frac{1}{3} \left(x+z+a\right) {/tex} ...(ii)

{tex} z = \frac{1}{4} \left(x+y+a\right) {/tex} ...(iii)

Also, x+ y+ z+a=60

Now, put the value of x + y + a = 4z

Then, 4z+ z = 60 => 52z = 60

Therefore, z = 12

Similarly, on putting the value of x + z + a = 3y, we get

3y + y = 60 => 4y = 60

Therefore, y = 15

Again, on putting the value of (y+ z+a) = 2x, we get

2x+ x=60 => 3x = 60

Therefore, x = 20

Now, x+ y+ z+a = 60

On putting the value of x,y and z, we get

12 + 15 + 20 + a = 60

Therefore, a = 60 - 47 = Rs.13

Explanation

Total number of students participated

= {tex} \frac{1}{4}B + \frac{3}{8}G {/tex}

Therefore, Required percentage

= = {tex} \left(\frac{\frac{1}{4}B + \frac{3}{8}G} {B+G}\right) \times 100\% {/tex}

Clearly, given data is inadequate.

Explanation

Let denominator of fraction = x

Then, numerator = x - 4

Therefore, Fraction = {tex} \frac{x - 4}{x} {/tex}

Now, according to the question,

{tex} 8 \left[\left(x - 4\right) - 2 \right] = \left(x + 1\right) {/tex}

{tex} \left(x - 4\right) - 2 = \frac{ \left(x + 1\right) }{8} {/tex}

=> 8x - 48 = x + 1

=> 8x - x = 48 + 1

=> 7x = 49

=> x = {tex} \frac{49}{7} {/tex}

Therefore, x = 7

Therefore, Fraction = {tex} \frac{7 - 4}{7} = \frac{3}{7} {/tex}

Explanation

LCM of 4, 5, 10 and 20 = 20

{tex} \sqrt[4]{2} = \left(2\right)^{\frac{1}{4}} = \left(2^{5}\right)^{\frac{1}{20}} = \left(32\right)^{\frac{1}{20}} {/tex}

{tex} \sqrt[5]{3} = \left(3\right)^{\frac{1}{5}} = \left(3^{4}\right)^{\frac{1}{20}} = \left(81\right)^{\frac{1}{20}} {/tex}

{tex} \sqrt[10]{6} = \left(6\right)^{\frac{1}{10}} = \left(6^{2}\right)^{\frac{1}{20}} = \left(36\right)^{\frac{1}{2}} {/tex}

{tex} \sqrt[20]{15} = \left(15\right)^{\frac{1}{20}} {/tex}

The greatest number is {tex} \left(81\right)^{\frac{1}{20}} i.e. \sqrt[5]{3} {/tex}

Explanation

If the fraction {tex} \frac{a}{b} {/tex} is positive, then ab > 0 must be true.

Explanation

Given, 1.5x = 0.04y

{tex} \frac{y}{x} = \frac{1.5}{0.004} = \frac{150}{4} = \frac{75}{2} {/tex}

{tex} \left(\frac{y - x}{y + x}\right) = \left(\frac{\frac{y}{x}-1}{\frac{y}{x}+1}\right) = \left(\frac{\frac{75}{2}-1}{\frac{75}{2}+1}\right) = \frac{73}{77} {/tex}

Explanation

Given, 1.5x = 0.04y

{tex} \frac{y}{x} = \frac{1.236}{0.764} = \frac{309}{191} {/tex}

{tex} \left(\frac{y - x}{y + x} \right) = \left(\frac{\frac{y}{x}-1}{\frac{y}{x}+1}\right) = \left(\frac{\frac{309}{191}-1}{\frac{309}{191}+1}\right) = \left(\frac{\frac{118}{191}}{\frac{500}{191}}\right) = \frac{118}{500} {/tex}= 0.236

Explanation

{tex} HCF \ of \ \frac{5}{8}, \frac{15}{8}, \frac{25}{32} {/tex}

= {tex} \frac{HCF \ of \ 5, 15 \ and \ 25} {LCM \ of \ 6, 8 \ and \ 32} = \frac{5}{96} = 0.052{/tex}