Question
Solve: $\frac{3 x}{4}+4 x=38$
✓
Answer
$\begin{aligned} & \frac{3 \mathrm{x}}{4}+4 \mathrm{x}=38 \\ & \Rightarrow \frac{3 \mathrm{x}}{4}+\frac{4 \mathrm{x}}{1}=38 \\ & \Rightarrow \frac{3 \mathrm{x}+16 \mathrm{x}}{4}=38 \\ & \Rightarrow 3 \mathrm{x}+16 \mathrm{x}=38 \times 4 \\ & \therefore 3 \mathrm{x}+16 \mathrm{x}=152 \\ & \Rightarrow 19 \mathrm{x}=152 \\ & \Rightarrow \mathrm{x}=\frac{152}{19}=8\end{aligned}$
$\therefore x=8$
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Five Students A, B, C, D, and E are competing in a long-distance race. Each student’s probability of winning the race is given below:
A → 20%, B → 22%, C → 7%, D → 15% and E → 36%
(i) Who is most likely to win the race?
(ii) Who is least likely to win the race?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
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(c) Find P(S’)
A → 20%, B → 22%, C → 7%, D → 15% and E → 36%
(i) Who is most likely to win the race?
(ii) Who is least likely to win the race?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
(b) State, in words, the complementary event S’.
(c) Find P(S’)
Use the given figure to express:
(i) $a$ in terms of $b$ and $f$;
(ii) $e$ in terms of $f$ and $g$;
(iii) $d$ in terms of $a$ and $e$;
(iv) $c$ in terms of $e$ and $g$.
→(i) $a$ in terms of $b$ and $f$;
(ii) $e$ in terms of $f$ and $g$;
(iii) $d$ in terms of $a$ and $e$;
(iv) $c$ in terms of $e$ and $g$.
A number is first decreased by 40% and then again decreased by 60%. Find the percentage increase or decrease on the whole.
Radhika is in the Chemistry Laboratory and is working on a practical. She mixed three salts A, B and C taking 150 gm of A and 300 gm each of B and C to prepare a mixture X.
Q.1. The percentage of salt A in mixture X is:
(a) 15% $\quad$$\quad$(b) 20% $\quad$$\quad$(c) 25%$\quad$$\quad$ (d) 30%
Q.2. By what percent is salt C more than salt A in mixture X?
(a) 50% $\quad$$\quad$(b) 100%$\quad$$\quad$ (c) 150% $\quad$$\quad$(d) 200%
Q.3. Radhika added 250 gm of salt B to mixture X to prepare a new mixture Y. By what per cent did salt B increase
(a) $63 \frac{1}{3} \%$$\quad$$\quad$ (b) $75 \%$ $\quad$$\quad$(c) $83 \frac{1}{3} \%$ $\quad$$\quad$(d) $121 \%$
Q.4. The percentage of salt A in mixture Y is :
(a) $15 \%$ $\quad$$\quad$(b) $17 \frac{1}{2} \%$ $\quad$$\quad$(c) $20 \%$$\quad$$\quad$ (d) $22 \frac{1}{2} \%$
→Q.1. The percentage of salt A in mixture X is:
(a) 15% $\quad$$\quad$(b) 20% $\quad$$\quad$(c) 25%$\quad$$\quad$ (d) 30%
Q.2. By what percent is salt C more than salt A in mixture X?
(a) 50% $\quad$$\quad$(b) 100%$\quad$$\quad$ (c) 150% $\quad$$\quad$(d) 200%
Q.3. Radhika added 250 gm of salt B to mixture X to prepare a new mixture Y. By what per cent did salt B increase
(a) $63 \frac{1}{3} \%$$\quad$$\quad$ (b) $75 \%$ $\quad$$\quad$(c) $83 \frac{1}{3} \%$ $\quad$$\quad$(d) $121 \%$
Q.4. The percentage of salt A in mixture Y is :
(a) $15 \%$ $\quad$$\quad$(b) $17 \frac{1}{2} \%$ $\quad$$\quad$(c) $20 \%$$\quad$$\quad$ (d) $22 \frac{1}{2} \%$
In $\triangle A B C, B A$ and $B C$ are produced. Find the angles $a$ and $h$. if $A B=$ BC.
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Q.1. Sanjay repairs an HP laptop of Mr Lal. He charges ₹ 950 for the work. How long did the repair work take place?
(a) 6 hours$\quad$$\quad$ (b) 7 hours$\quad$$\quad$ (c) 8 hours$\quad$$\quad$ (d) 9 hours
Q.2. Sanjay repairs a Dell laptop of Mr Gupta. The total charges were ₹ 830. How long did the repair work take place?
(a) 5 hours $\quad$$\quad$(b) 6 hours$\quad$$\quad$ (c) 7 hours $\quad$$\quad$(d) 8 hours
Q.3. He repairs an HP laptop and a Dell laptop of Mr Subhash. He found that the repair work for both the laptops took equal time and also the service charges of the two laptops were the same. How long did the repair work take place for each laptop?
(a) 6 hours $\quad$$\quad$(b) 7 hours$\quad$$\quad$ (c) 8 hours$\quad$$\quad$ (d) 9 hours
Q.4. What were the total service charges that Mr. Subhash had to pay for both the laptops ?
(a) ₹ 1040 $\quad$$\quad$(b) ₹ 1260 $\quad$$\quad$(c) ₹ 2040$\quad$$\quad$ (d) ₹ 2520
→Q.1. Sanjay repairs an HP laptop of Mr Lal. He charges ₹ 950 for the work. How long did the repair work take place?
(a) 6 hours$\quad$$\quad$ (b) 7 hours$\quad$$\quad$ (c) 8 hours$\quad$$\quad$ (d) 9 hours
Q.2. Sanjay repairs a Dell laptop of Mr Gupta. The total charges were ₹ 830. How long did the repair work take place?
(a) 5 hours $\quad$$\quad$(b) 6 hours$\quad$$\quad$ (c) 7 hours $\quad$$\quad$(d) 8 hours
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Q.4. What were the total service charges that Mr. Subhash had to pay for both the laptops ?
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Evaluate: $\left(\frac{7}{8} \times \frac{24}{21}\right)+\left(\frac{-5}{9} \times \frac{6}{-25}\right)$
→Find the mean height of 65 boys from the following data :
| Height (in cm) | 142 | 144 | 146 | 148 | 150 | 152 |
| Number of boys | 10 | 13 | 12 | 7 | 17 | 6 |
Find the solution set of inequation : $2-x<4 x-7<11-2 x, x \in Z$
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