Simplification - Study Mode

[#216] Find the simplest value of $$frac{{6.25 - 1.96}}{{1.1}}.$$
Correct Answer

(B) 3.9

Explanation

Solution: $$eqalign{
& frac{{6.25 - 1.96}}{{1.1}} cr
& = frac{{{{left( {2.5}
ight)}^2} - {{left( {1.4}
ight)}^2}}}{{left( {1.1}
ight)}} cr
& = frac{{left( {1.1}
ight) imes 3.9}}{{left( {1.1}
ight)}} cr
& = 3.9{ ext{ Answer}} cr} $$

[#217] Find the value of $$225 - left[ {42 - left{ {25 - left( {18 - overline {18 + 13} }
ight)}
ight}}
ight].$$
Correct Answer

(B) 221

Explanation

Solution: $$eqalign{
& 225 - left[ {42 - left{ {25 - left( {18 - overline {18 + 13} }
ight)}
ight}}
ight] cr
& = 225 - left[ {42 - left{ {25 - left( {18 - 18 - 13}
ight)}
ight}}
ight] cr
& = 225 - left[ {42 - left{ {25 + 13}
ight}}
ight] cr
& = 225 - left[ {42 - 38}
ight] cr
& = 221 cr} $$

[#218] The value of $$frac{{33}}{{40}} + frac{1}{5}left[ {frac{4}{5} - frac{1}{5} imes left( {frac{7}{8} - frac{5}{4}}
ight)}
ight]$$ xa0 xa0xa0 is:
Correct Answer

(D) 1

Explanation

Solution: $$eqalign{
& frac{{33}}{{40}} + frac{1}{5}left[ {frac{4}{5} - frac{1}{5} imes left( {frac{7}{8} - frac{5}{4}}
ight)}
ight] cr
& = frac{{33}}{{40}} + frac{1}{5}left[ {frac{4}{5} - frac{1}{5} imes left( {frac{{7 - 10}}{8}}
ight)}
ight] cr
& = frac{{33}}{{40}} + frac{1}{5}left[ {frac{4}{5} + frac{1}{5} imes frac{3}{8}}
ight] cr
& = frac{{33}}{{40}} + frac{1}{5}left[ {frac{4}{5} + frac{3}{{40}}}
ight] cr
& = frac{{33}}{{40}} + frac{1}{5}left[ {frac{{32 + 3}}{{40}}}
ight] cr
& = frac{{33}}{{40}} + frac{7}{{40}} cr
& = frac{{40}}{{40}} cr
& = 1 cr} $$

[#219] In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Correct Answer

(B) 175

Explanation

Solution: Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 * 8 * 4) = 160. ∴ 160 * 2.40 + x * 3.20 = 432 ⇒ 3.20 x = 432 - 384 = 48 ⇒ x = 15. Hence, total hours of work = (160 + 15) = 175.

[#220] Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
Correct Answer

(C) 512

Explanation

Solution: Explanation 1 $$eqalign{
& { ext{Let number of children}} = n cr
& { ext{Then, number of books each child will get }} = frac{n}{8} cr
& { ext{Total books distributed}} = n imes frac{n}{8} = frac{{{n^2}}}{8} cr
& { ext{If the number children}} = frac{n}{2}, cr
& { ext{number of books each child will get}} = 16 cr
& { ext{Total books distributed }} = frac{n}{2} imes 16 = 8n{ ext{ }} cr
& herefore frac{{{n^2}}}{8} = 8n cr
& Rightarrow frac{n}{8} = 8 cr
& Rightarrow n = 64 cr
& { ext{Total number of books distributed}} cr
& = 8n = 8 imes 64 = 512 cr} $$ Explanation 2 If number of children was half, each child would have got 16 books. Therefore, actually each child got $$frac{{16}}{2}$$ = 8 Books And the number of children is 8 × 8 = 64 Hence, total number of books distributed = 64 × 8 = 512 Explanation 3 Let number of children $$ = n$$ Then, number of books each child will get $$ = frac{n}{8}$$ If the number children $$ = frac{n}{2}$$, number of books each child will get $$ = 16$$ More children, less books (indirect proportion). Therefore, $$eqalign{
& n : frac{n}{2} = 16 : frac{n}{8} cr
& Rightarrow frac{{{n^2}}}{8} = 8n cr
& Rightarrow frac{n}{8} = 8 cr
& Rightarrow n = 64 cr} $$ Therefore, total number of books distributed = 8n = 8 × 64 = 512