| **Answers & Solutions ** | | 1 . | Answer : Option C | Explanation : | Let Amit's spped be x key depressions per day. Sujit's speed $4x\over 5$ key depressions per day 5$\times$ + 5 $\times$ $4x\over 5$ = 576000 $\Rightarrow$ 9 $x$ = 576000 $\Rightarrow$ $x$ = $576000\over 9$ = 64000 Amit's speed per hour = $64000\over 8$= 8000 | | | 2 . | Answer : Option A | Explanation : | 4 × 2 men $\cong $4 × 4 women = 20 children 2 men $\cong $ 4 women $\cong $ 5 children 2 men + 4 women + 10 children = 20 children $M_1 D_1 = M_2 D_2$ 5 x 4 = 20 x D$_2$ $\Rightarrow$ D$_2$ = 1 day | | | 3 . | Answer : Option D | Explanation : | Days $\,\,\,\,\,\,\,\,\,$ Men 10$\uparrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$12$\downarrow$ $\,$ 8$\uparrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ $x$$\downarrow$ Where $x$= No. of Men 8 : 10 :: 12 : $x$ $\Rightarrow$ $8 \times x = 10 \times 12 $ $\Rightarrow$ x = $10 + 12\over 8$ = 15 | | | 4 . | Answer : Option C | Explanation : | A’s 1 day’s work = $1\over 12$ (A + B)’s 1 day’s work = $1\over 8$ B’s 1 day’s work = $1 \over 8$ - $1\over 12$ = $3 - 2 \over 24$ = $1\over 24$ B alone can do the work in 24 days. | | | 5 . | Answer : Option B | Explanation : | In 36 days 12 men can do 1 complete work. In 36 days 12 women can do $3\over 4$ th of the work Since time and the no, of persons in the same is both casses, 1 woman’s daily work $3\over 4$ th of 1 man’s daily work 8 woman’s daily work = $3\over 4$ × 8 = 6 meri’s daily work (10 men + 8 womens daily work) = (10 men + 6 men) = 16 men’s daily work. 12 men can do the work is 36 days 16 men can do the work is 36 × $12\over 16$ = 27 days. | | | 6 . | Answer : Option B | Explanation : | 2 men = 1 woman 1 man = $1\over 2$ women 3 men = $3\over 2$ women Again, 2 children = 1 man = $1\over 2$ women 1 child = $1\over 4$ women 6 children = $6\over 4$ = $3\over 2$ women Now, three men, four women and six children = $3\over 2$ + 4 + $3\over 2$ = 7 women Hence, 7 women complete the work in 7 days
| | | 7 . | Answer : Option B | Explanation : | Work done in 1st two days = $1 \over 10$ + $1\over 15$ = $ 3 + 2 \over 30$ = $1 \over 6$ Number of days = 12 | | | 8 . | Answer : Option D | Explanation : | $M_1D_1\over W_1$ = $M_2D_2\over W_2$ $\Rightarrow$ $ 6\times 6\over W_1 $ = $9 \times 10 \over 1$ $\Rightarrow$ $W_1$ = $6 \times 6\over 9 \times 10$ = $2\over 5$ Part of work done by 6 women in 6 days = $2 \over 5$ Part of work done by 6 men in 6 days = 1 – $2 \over 5$ = $3 \over 5$ $M_1D_1\over W_1$ = $M_2D_2\over W_2$ $\Rightarrow$ $ 6\times 6\over W_1 $ $\Rightarrow$ $6 \times 6 \over {3\over 5}$ = $ 15 \times D_2 \over 1$ $\Rightarrow$ $15 \times D_2$ = $ 6 \times 6 \times 5\over 3$ = 60 $\Rightarrow$ $D_2$ = $60\over 15$ = 4 day
| | | 9 . | Answer : Option C | Explanation : | Examiners$\,\,\,\,\,\,\,\,\,\,$ Work$\,\,\,\,\,\,\,\,\,\,$ Days$\,\,\,\,\,\,\,\,\,\,$ Hours / day $\,\,\,\,\,\,\,\,\,\,$4$\uparrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$1$\downarrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$10$\uparrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$5$\downarrow$ $\,\,\,\,\,\,\,\,\,\,$2$\uparrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$2$\downarrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$20$\uparrow$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$x$$\downarrow$ (2 : 4), (1 : 2) & (20 : 10) :: (5 : $x$) $\Rightarrow$$2 \times 20 \times x= 4 × 10 × 5 × 2$ $\Rightarrow$ $x$ = $4 \times 10 \times 5 \times 2 \over 2\times 20$ = 10 hours | | | | |

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