100 simplification questions with solutions
simplification questions
1. \(\displaystyle \frac{9}{{10}}+\frac{3}{{11}}+\frac{7}{{15}}=?\)
(a) \(\displaystyle 1\frac{{217}}{{330}}\)
(b) \(\displaystyle 1\frac{{221}}{{330}}\)
(c) \(\displaystyle 1\frac{{211}}{{330}}\)
(d) \(\displaystyle 1\frac{{197}}{{330}}\)
(e) None of these
Solution: (c)
\(\displaystyle ?=\frac{9}{{10}}+\frac{3}{{11}}+\frac{7}{{15}}=\frac{{297+90+154}}{{330}}\)
= \(\displaystyle \frac{{541}}{{330}}=1\frac{{211}}{{330}}\)
2. \(\displaystyle \frac{{57}}{{67}}\times \frac{{32}}{{171}}\times \frac{{45}}{{128}}=?\)
(a) \(\displaystyle \frac{{15}}{{262}}\)
(b) \(\displaystyle \frac{{15}}{{268}}\)
(c) \(\displaystyle \frac{{15}}{{266}}\)
(d) \(\displaystyle \frac{{17}}{{268}}\)
(e) None of these
Solution: (b)
\(\displaystyle ?=\frac{{57}}{{67}}\times \frac{{32}}{{171}}\times \frac{{45}}{{128}}=\frac{{15}}{{268}}\)
3. \(\displaystyle \frac{1}{4}of\frac{1}{2}of\frac{3}{4}of52000=?\)
(a) 4875
(b) 4857
(c) 4785
(d) 4877
(e) None of these
Solution: (a)
\(\displaystyle ?=52000\times \frac{3}{4}\times \frac{1}{2}\times \frac{1}{4}=4875\)
4. 38% of 4500 – 25% of ? = 1640
(a) 260
(b) 270
(c) 280
(d) 290
(e) None of these
Solution: (c)
\(\displaystyle \frac{{4500\times 38}}{{100}}-\frac{{?\times 25}}{{100}}=1640\)
\(\displaystyle \Rightarrow \)\(\displaystyle 1710-\frac{?}{4}=1640\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{?}{4}=1710-1640=70\)
Therefore, \(\displaystyle ?=4\times 70=280\)
5. \(\displaystyle (5863-\sqrt{{2704}})\times 0.5=?\)
(a) 2955.5
(b) 2905.5
(c) 2590.5
(d) 2909.5
(e) None of these
Solution: (b)
\(\displaystyle ?=(5863-\sqrt{{2704}})\times 0.5\)
\(\displaystyle ?=(5863-52)\times 0.5\)
\(\displaystyle ?=5811\times 0.5=2905.5\)
6. \(\displaystyle 283\times 56+252=20\times ?\)
(a) 805
(b) 803
(c) 807
(d) 809
(e) None of these
Solution: (a)
\(\displaystyle 283\times 56+252=20\times ?\)
\(\displaystyle \Rightarrow \)\(\displaystyle 15848+252=20\times ?\)
\(\displaystyle \Rightarrow \)\(\displaystyle 16100=20\times ?\)
Therefore, \(\displaystyle ?=\frac{{16100}}{{20}}=805\)
7. \(\displaystyle 526\times 12+188=50\times ?\)
(a) 120
(b) 160
(c) 140
(d) 110
(e) None of these
Solution: (e)
\(\displaystyle 526\times 12+188=50\times ?\)
\(\displaystyle 6312+188=50\times ?\)
\(\displaystyle 6500=50\times ?\)
\(\displaystyle ?=\frac{{6500}}{{50}}=130\)
8. ?% of 5600 –28% of 3500 = 1988
(a) 58
(b) 55
(c) 51
(d) 53
(e) None of these
Solution: (d)
\(\displaystyle \frac{{5600\times ?}}{{100}}-\frac{{3500\times 28}}{{100}}=1988\)
\(\displaystyle 56\times ?-980=1988\)
\(\displaystyle 56\times ?=1988+980=2968\)
\(\displaystyle ?=\frac{{2968}}{{56}}=53\)
9. \(\displaystyle 2\frac{4}{5}-1\frac{3}{8}+3\frac{1}{2}=?\)
(a) \(\displaystyle 4\frac{{17}}{{40}}\)
(b) \(\displaystyle 4\frac{{37}}{{40}}\)
(c) \(\displaystyle 3\frac{{27}}{{40}}\)
(d) \(\displaystyle 3\frac{{11}}{{40}}\)
(e) None of these
Solution: (b)
\(\displaystyle ?=2+\frac{4}{5}-1-\frac{3}{8}+3+\frac{1}{2}\)
\(\displaystyle (2-1+3)+(\frac{4}{5}-\frac{3}{8}+\frac{1}{2})\)
\(\displaystyle 4+\frac{{32-15+20}}{{40}}=4+\frac{{37}}{{40}}=4\frac{{37}}{{40}}\)
10. \(\displaystyle {{(49)}^{2}}\times {{(7)}^{8}}+{{(343)}^{3}}={{(7)}^{?}}\)
(a) 3
(b) 11
(c) 7
(d) 9
(e) None of these
Solution: (a)
\(\displaystyle {{(49)}^{2}}\times {{7}^{8}}\div {{(343)}^{3}}={{7}^{?}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle {{({{7}^{2}})}^{2}}\times {{7}^{8}}\div {{({{7}^{3}})}^{3}}={{7}^{?}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle {{7}^{4}}\times {{7}^{8}}\div {{7}^{9}}={{7}^{?}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle {{7}^{{4+8-9}}}={{7}^{?}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle {{7}^{3}}={{7}^{?}}\Rightarrow ?=3\)
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