Decimal Fraction - Study Mode

[#71] $$frac{{4.2 imes 4.2 - 1.9 imes 1.9}}{{2.3 imes 6.1}}$$ xa0xa0 is equal to:
Correct Answer

(B) 1

Explanation

Solution: $$eqalign{
& ext{Let } a = 4.2 ext{ and } b = 1.9 cr
& { ext{Given Expression}} cr
& = frac{{ {{a^2} - {b^2}} }}{{left( {a + b}
ight)left( {a - b}
ight)}} cr
& = frac{{ {{a^2} - {b^2}} }}{{ {{a^2} - {b^2}} }} cr
& = 1 cr} $$

[#72] If $$frac{{144}}{{0.144}} = frac{{14.4}}{x},$$ xa0 then the value of x is:
Correct Answer

(A) 0.0144

Explanation

Solution: $$eqalign{
& frac{{144}}{{0.144}} = frac{{14.4}}{x} cr
& Rightarrow frac{{144 imes 1000}}{{144}} = frac{{14.4}}{x} cr
& Rightarrow x = frac{{14.4}}{{1000}} cr
& ,,,,,,,,,,,,,, = 0.0144 cr} $$

[#73] The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
Correct Answer

(B) 2011

Explanation

Solution: Suppose commodity X will cost 40 paise more than Y after z years Then,(4.20 + 0.40z) − (6.30 + 0.15z) = 0.40 ⇒ 0.25z = 0.40 + 2.10 $$eqalign{
& Rightarrow z = frac{{2.50}}{{0.25}} cr
& ,,,,,,,,,,,,, = frac{{250}}{{25}} cr
& ,,,,,,,,,,,,, = 10 cr} $$ ∴ X will cost 40 paise more than Y 10 years After 2001 i.e., 2011

[#74] Which of the following are in descending order of their value ?
Correct Answer

(D) $$frac{6}{7},frac{5}{6},frac{4}{5},frac{3}{7},frac{2}{5},frac{1}{3}$$

Explanation

Solution: Converting each of the given fractions in to decimal form, we get $$eqalign{
& frac{1}{3} = 0.33 cr
& frac{2}{5} = 0.4 cr
& frac{3}{7} = 0.42 cr
& frac{4}{5} = 0.8 cr
& frac{5}{6} = 0.83 cr
& frac{6}{7} = 0.85 cr} $$ Clearly, 0.85 > 0.83 > 0.8 > 0.42 > 0.4 > 0.33 So, $$frac{6}{7}$$ > $$frac{5}{6}$$ > $$frac{4}{5}$$ > $$frac{3}{7}$$ > $$frac{2}{5}$$ > $$frac{1}{3}$$

[#75] Which of the following fractions is greater than $$frac{{3}}{{4}}$$ and less than $$frac{{5}}{{6}}$$ ?
Correct Answer

(C) $$frac{{4}}{{5}}$$

Explanation

Solution: $$eqalign{
& frac{3}{4} = 0.75,{kern 1pt} cr
& frac{5}{6} = 0.833,{kern 1pt} cr
& frac{1}{2} = 0.5, cr
& frac{2}{3} = 0.66, cr
& {kern 1pt} frac{4}{5} = 0.8, cr
& frac{9}{{10}} = 0.9 cr} $$ Clearly, 0.8 lies between 0.75 and 0.833 $$ herefore frac{4}{5}{ ext{lies between}}frac{3}{4}{ ext{and}}frac{5}{6}$$