Question 15 Marks
Mr. Mehra gave one-third of his money to his son, one-fifth of his money to his daughter, and the remaining amount to his wife. If his wife got $Rs. 91,000,$ how much money did Mr. Mehra have originally?
AnswerLet Mr. Mehra has money $=1$
Money given to his son $=\frac{1}{3}$
and the money given to his daughter $=\frac{1}{5}$
$\therefore$ Remaining money given to his wife
$=1-\left(\frac{1}{3}+\frac{1}{5}\right) $
$=1-\frac{5+3}{15} $
$=1-\frac{8}{15} $
$=\frac{15-8}{15} $
$=\frac{7}{15} $
$\therefore \frac{7}{15} \text { of his money }=\text { Rs. } 91000 $
$\therefore \text { Total money }=\text { Rs. } \frac{91000 \times 15}{7} $
$=\text { Rs. } 13,000 \times 15 $
$=\text { Rs. } 1,95,000$
View full question & answer→Question 25 Marks
Evaluate:
$8-\left\{5 \frac{1}{3}-\left(3-2 \frac{1}{2}\right)\right\}$
Answer$8-\left\{5 \frac{1}{3}-\left(3-2 \frac{1}{2}\right)\right\} $
$=8-\left\{\frac{16}{3}-\left(3-\frac{5}{2}\right)\right\} $
$=8-\left\{\frac{16}{3}-3+\frac{5}{2}\right\} $
$=\frac{8}{1}-\frac{16}{3}+\frac{3}{1}-\frac{5}{2} $
$=\frac{48-32+18-15}{6} $
$=\frac{48+18-32-15}{6} $
$=\frac{66-47}{6} $
$=\frac{19}{6} $
$=3 \frac{1}{6}$
View full question & answer→Question 35 Marks
Evaluate:
$1 \frac{4}{13} \text { of } 2 \frac{2}{7} \div \frac{68}{91}-\left(1 \frac{1}{2}-1 \frac{1}{3}\right)$
Answer$1 \frac{4}{13} \text { of } 2 \frac{2}{7} \div \frac{68}{91}-\left(1 \frac{1}{2}-1 \frac{1}{3}\right) $
$=\frac{17}{13} \text { of } \frac{16}{7} \div \frac{68}{91}-\left(\frac{3}{2}-\frac{4}{3}\right) $
$=\frac{17}{13} \text { of } \frac{16}{7} \div \frac{68}{91}-\frac{3}{2}+\frac{4}{3} \ldots \ldots . . . \text { (remove bracket) } $
$=\frac{272}{91} \div \frac{68}{91}-\frac{3}{2}+\frac{4}{3} \ldots \ldots \ldots .(\text { remove 'of') } $
$=\frac{272}{91} \times \frac{91}{68}-\frac{3}{2}+\frac{4}{3} $
$=\frac{4}{1}-\frac{3}{2}+\frac{4}{3} \ldots \ldots . .(\text { remove ' } \times \text { ') } $
$=\frac{24-9+8}{6} $
$=\frac{32-9}{6} $
$=\frac{23}{6} $
$=3 \frac{5}{6}$
View full question & answer→Question 45 Marks
Evaluate:
$\frac{1}{3}+\frac{7}{9} \div\left(\frac{7}{10} \times 1 \frac{1}{4}\right)$
Answer$\frac{1}{3}+\frac{7}{9} \div\left(\frac{7}{10} \times 1 \frac{1}{4}\right) $
$=\frac{1}{3}+\frac{7}{9} \div\left(\frac{7}{10} \times \frac{5}{4}\right) $
$=\frac{1}{3}+\frac{7}{9} \div \frac{7}{8} \ldots . .(\text { remove bracket }) $
$=\frac{1}{3}+\frac{7}{9} \times \frac{8}{7} \ldots \ldots . .(\text { remove } \div) $
$=\frac{1}{3}+\frac{8}{9} $
$=\frac{3+8}{9} $
$=\frac{11}{9} $
$=1 \frac{2}{9}$
View full question & answer→Question 55 Marks
Evaluate:
$3 \frac{5}{6}-1 \frac{4}{15}-\left(3 \frac{2}{9}-1 \frac{3}{5}\right)$
Answer$3 \frac{5}{6}-1 \frac{4}{15}-\left(3 \frac{2}{9}-1 \frac{3}{5}\right) $
$=\frac{23}{6}-\frac{19}{15}-\left(\frac{29}{9}-\frac{8}{5}\right) $
$=\frac{23}{6}-\frac{19}{15}-\frac{29}{9}+\frac{8}{5} $
$=\frac{345-114-290+144}{90} \ldots \ldots \ldots . .(\text { L.C.M. of } 6,15,9,5=90) $
$=\frac{345+144-114-290}{90} $
$=\frac{489-404}{90} $
$=\frac{85}{90} $
$=\frac{85 \div 5}{90 \div 5} $
$=\frac{17}{18}$
View full question & answer→Question 65 Marks
$\text { Show that } \frac{4}{5} \text { lies between } \frac{3}{4} \text { and } \frac{5}{6} \text {. }$
Answer$\frac{3}{4}>\frac{4}{5}>\frac{5}{6} \text { or } \frac{3}{4}<\frac{4}{5}<\frac{5}{6}$
Now L.C.M. of $4, 5, 6=60$
$\therefore \frac{3}{4}=\frac{3 \times 15}{4 \times 15}=\frac{45}{60} $
$\frac{4}{5}=\frac{4 \times 12}{5 \times 12}=\frac{48}{60} $
$\frac{5}{6}=\frac{5 \times 10}{6 \times 10}=\frac{50}{60} $
$\therefore \frac{45}{60}<\frac{48}{60}<\frac{50}{60} $
$\Rightarrow \frac{3}{4}<\frac{4}{5}<\frac{5}{6}$
Hence $\frac{4}{5}$ lies between $\frac{3}{4}$ and $\frac{5}{6}$
View full question & answer→Question 75 Marks
Simplify:
$\left(1 \div 3 \frac{1}{3}\right) \times 3 \frac{1}{3} \text { of } 7 \frac{2}{9}-6$
Answer$\left(1 \div 3 \frac{1}{3}\right) \times 3 \frac{1}{3} \text { of } 7 \frac{2}{9}-6 $
$=\left(1 \div \frac{10}{3}\right) \times \frac{10}{3} \text { of } \frac{65}{9}-6 $
$=\left(1 \times \frac{3}{10}\right) \times \frac{10}{3} \text { of } \frac{65}{9}-6 $
$=\frac{3}{10} \times \frac{10}{3} \text { of } \frac{65}{9}-6 \ldots \ldots . .(\text { Removing bracket }) $
$=\frac{3}{10} \times \frac{650}{27}-\frac{6}{1} \ldots \ldots . . . .(\text { Removing 'of') } $
$=\frac{65}{9}-\frac{6}{1} \ldots \ldots \ldots \ldots . . .(\text { Removing ' } \times \text { ') } $
$=\frac{65-54}{9} $
$=\frac{11}{9} $
$=1 \frac{2}{9}$
View full question & answer→Question 85 Marks
$\text { Show that } \frac{3}{7} \text { lies between } \frac{2}{5} \text { and } \frac{5}{7} \text {. }$
Answer$\frac{3}{7}$ will lies between $\frac{2}{5}$ and $\frac{5}{7}$ if
$\frac{2}{5}>\frac{3}{7}>\frac{5}{7} \text { or } \frac{2}{5}<\frac{3}{7}<\frac{5}{7}$
Now, comparing $\frac{2}{5}, \frac{3}{7}, \frac{5}{7}$
L.C.M. of $5$ and $7=35$
$\therefore \frac{2}{5}=\frac{2 \times 7}{5 \times 7}=\frac{14}{35} $
$\frac{3}{7}=\frac{3 \times 5}{7 \times 5}=\frac{15}{35}$
$\text { and } \frac{5}{7}=\frac{5 \times 5}{7 \times 5}=\frac{25}{35} $
$\therefore \frac{14}{35}<\frac{15}{35}<\frac{25}{35} $
$\frac{2}{5}<\frac{3}{7}<\frac{5}{7} $
$\frac{3}{7} \text { lies between } \frac{2}{5} \text { and } \frac{5}{7}$
View full question & answer→Question 95 Marks
I bought wheat worth Rs. $12 \frac{1}{2}$, rice worth Rs. $25 \frac{3}{4}$ and vegetables worth Rs. $10 \frac{1}{4}$. If I gave a hundred rupee note to the shopkeeper; how much did he return to me?
Answer$\text { Money given to shopkeeper }=\text { Rs. } 100 $
$\text { Total amount of goods bought } $
$=\text { Rs. }\left(12 \frac{1}{2}+25 \frac{3}{4}+10 \frac{1}{4}\right) \ldots . . . \text { (Wheat, Rice, and Vegetable) } $
$=\frac{25}{2}+\frac{103}{4}+\frac{41}{4} $
$=\frac{25 \times 2}{2 \times 2}+\frac{103}{4}+\frac{41}{4} $
$=\frac{50}{4}+\frac{103}{4}+\frac{41}{4} $
$=\frac{50+103+41}{4} $
$=\text { Rs. } \frac{194}{4}$
$\therefore$ Money returned by shopkeeper
$=\text { Rs. }\left(100-\frac{194}{4}\right)$
By taking LCM,
$=\text { Rs. } \frac{400-194}{4}$
$=\frac{206}{4} $
$=\text { Rs. } \frac{103}{2}$
$=\text { Rs. } 51 \frac{1}{2} \text {. }$
View full question & answer→Question 105 Marks
In a particular month, a man earns $Rs. 7,200.$ Out of this income, he spends $\frac{3}{10}$ on food, $\frac{1}{4}$ on house rent, $\frac{1}{10}$ on insurance, and $\frac{2}{25}$ on holidays. How much did he save in that month?
AnswerEarning of a man in a particular month $= Rs. 7200$
Amount spent on food $=\frac{3}{10}$ of $Rs. 7200$
$\text { = Rs. } 2160$
Amount spent on house rent
$=\frac{1}{4} \text { of Rs. } 7200 $
$=\text { Rs. } 1800$
Amount spent on insurance
$=\frac{1}{10} \text { of } R $
$=\text { Rs. } 720$
Amount spent on holidays
$=\frac{2}{25}$ of $Rs. 7200$
$= Rs. 2 \times 288$
$= Rs. 576$
$\therefore$ Total amount spent $=$ Rs. $(2160+1800+720+576)= Rs. 5256$
$\therefore$ Amount saved $= Rs. 7200- Rs. 5256= Rs. 1944$
View full question & answer→Question 115 Marks
When Ajit travelled 15 km, he found that one-fourth of his journey was still left. What was the full length of the journey?
AnswerLet the total length of journey $=x$
Journey travelled $=15 km$
Journey still left $=\frac{1}{4}$ of $x$
Now, according to question,
$x-15=\frac{1}{4}$ of $x$
$x-15=\frac{x}{4}$
$x-\frac{x}{4}=15$
$\frac{4 x-x}{4}=15$
$3 x=15 \times 4$
$x=\frac{15 \times 4}{3}$
$=20 km$
$\therefore$ Total length of the journey $=20 km$.
View full question & answer→Question 125 Marks
Add the following fractions:
$3 \frac{1}{8}, 5 \frac{5}{12} \text { and } \frac{5}{16}$
Answer$3 \frac{1}{8}+5 \frac{5}{12}+\frac{5}{16} $
$=\frac{3 \times 8+1}{8}+\frac{5 \times 12+5}{12}+\frac{5}{16} $
$\left.=\frac{25}{8}+\frac{65}{12}+\frac{5}{16} \ldots \ldots . . \text { (L.C.M. of } 8,12 \text { and } 16 \text { is } 48\right) $
$=\frac{25 \times 6}{8 \times 6}+\frac{65 \times 4}{12 \times 4}+\frac{5 \times 3}{16 \times 3} $
$=\frac{150}{48}+\frac{260}{48}+\frac{15}{48} $
$=\frac{150+260+15}{48} $
$=\frac{425}{48}=8 \frac{41}{48}$
View full question & answer→Question 135 Marks
Arrange the given fractions in ascending order of magnitude:
$\frac{2}{3}, \frac{5}{9}, \frac{5}{6}, \frac{3}{8}$
Answer$\frac{2}{3}, \frac{5}{9}, \frac{5}{6}, \frac{3}{8}$
L.C.M. of denominator $3,9,6,8=72$
| $2$ |
$3,$ |
$9,$ |
$6,$ |
$8$ |
| $3$ |
$3,$ |
$9,$ |
$3,$ |
$4$ |
| |
$1,$ |
$3,$ |
$1,$ |
$4$ |
$=2 \times 3 \times 3 \times 4=72$
$\therefore \frac{2}{3}=\frac{2 \times 24}{3 \times 24}=\frac{48}{72} ; \frac{5}{9}=\frac{5 \times 8}{9 \times 8}=\frac{40}{72} $
$\frac{5}{6}=\frac{5 \times 12}{6 \times 12}=\frac{60}{72} ; \frac{3}{8}=\frac{3 \times 9}{8 \times 9}=\frac{27}{72}$
Arranging in ascending order,
$\frac{27}{72}, \frac{40}{72}, \frac{48}{72}, \frac{60}{72}$
i.e. $\frac{3}{8}, \frac{5}{9}, \frac{2}{3}, \frac{5}{6}$ View full question & answer→Question 145 Marks
Arrange the given fractions in ascending order of magnitude:
$\frac{9}{16}, \frac{7}{12}, \frac{1}{4}$
Answer$\frac{9}{16}, \frac{7}{12}, \frac{1}{4}$
L.C.M. of denominator $16,12,4=48$
| $4$ |
$16,$ |
$12,$ |
$4$ |
| $4$ |
$4,$ |
$3,$ |
$1$ |
| $3$ |
$1,$ |
$3,$ |
$1$ |
| |
$1,$ |
$1,$ |
$1$ |
$=4 \times 4 \times 3=48$
$\therefore \frac{9}{16}=\frac{9 \times 3}{16 \times 3}=\frac{27}{48} ; \frac{7}{12}=\frac{7 \times 4}{12 \times 4}=\frac{28}{48} $
$\frac{1}{4}=\frac{1 \times 12}{4 \times 12}=\frac{12}{48}$
Arranging in ascending order,
$\frac{12}{48}, \frac{27}{48}, \frac{28}{48}$
i.e. $\frac{1}{4}, \frac{9}{16}, \frac{7}{12}$ View full question & answer→Question 155 Marks
Arrange the given fractions in descending order of magnitude:
$\frac{5}{7}, \frac{3}{8}, \frac{9}{11}$
Answer$\frac{5}{7}, \frac{3}{8}, \frac{9}{11}$
L.C.M. of numerator 5, 3, $9=45$
| $3$ |
$5,$ |
$3,$ |
$9$ |
| $5$ |
$5,$ |
$1,$ |
$3$ |
| $3$ |
$1,$ |
$1,$ |
$3$ |
| |
$1,$ |
$1,$ |
$1$ |
$=3 \times 5 \times 3=45$
$\therefore \frac{5}{7}=\frac{5 \times 9}{7 \times 9}=\frac{45}{63} ; \frac{3}{8}=\frac{3 \times 15}{8 \times 15}=\frac{45}{120} $
$\frac{9}{11}=\frac{9 \times 5}{11 \times 5}=\frac{45}{55}$
We know that the numerator being the same, the fraction having the smallest denominator is the biggest fraction.
$\therefore \frac{45}{55}, \frac{45}{63}, \frac{45}{120}$
i.e. $\frac{9}{11}, \frac{5}{7}, \frac{3}{8}$ View full question & answer→Question 165 Marks
Arrange the given fractions in descending order of magnitude:
$\frac{5}{16}, \frac{13}{24}, \frac{7}{8}$
Answer$\frac{5}{16}, \frac{13}{24}, \frac{7}{8}$
| 2 |
16, |
24, |
8 |
| 2 |
8, |
12, |
4 |
| 2 |
4, |
6, |
2 |
| 2 |
2, |
3, |
1 |
| 3 |
1, |
3, |
1 |
| |
1, |
1, |
1 |
$\therefore \text { L.C.M. of } 16,24,8=2 \times 2 \times 2 \times 2 \times 3=48$
L.C.M. of denominator $16,24,8=48$
Converting into like fractions
$\frac{5}{16}=\frac{5 \times 3}{16 \times 3}=\frac{15}{48} ; \frac{13}{24}=\frac{13 \times 2}{24 \times 2}=\frac{26}{48}$
$\frac{7}{8}=\frac{7 \times 6}{8 \times 6}=\frac{42}{48}$
Now, arranging in descending order
$\frac{7}{8}, \frac{13}{24}, \frac{5}{16}$ View full question & answer→Question 175 Marks
Change the following groups of fractions to like fractions:
$\frac{2}{7}, \frac{7}{8}, \frac{5}{14}, \frac{9}{16}$
Answer$\frac{2}{7}, \frac{7}{8}, \frac{5}{14}, \frac{9}{16}$
L.C.M. of denominators $7, 8, 14, 16=112$
| $2$ |
$7,$ |
$8,$ |
$14,$ |
$16$ |
| $7$ |
$7,$ |
$4,$ |
$7,$ |
$8$ |
| $4$ |
$1,$ |
$4,$ |
$1,$ |
$8$ |
| |
$1,$ |
$1,$ |
$1,$ |
$2$ |
$=2 \times 7 \times 4 \times 2=112$
Now,$\frac{2}{7}=\frac{2 \times 16}{7 \times 16}=\frac{32}{112} ; \frac{7}{8}=\frac{7 \times 14}{8 \times 14}$
$=\frac{98}{112} ; \frac{5}{14}=\frac{5 \times 8}{14 \times 8}=\frac{40}{112} ; \frac{9}{6} $
$=\frac{9 \times 7}{16 \times 7}=\frac{63}{112}$
$\therefore \frac{2}{7}, \frac{7}{8}, \frac{5}{14}, \frac{9}{16}=\frac{32}{112}, \frac{98}{112}, \frac{40}{112}, \frac{63}{112}$ View full question & answer→Question 185 Marks
Change the following groups of fractions to like fractions:
$\frac{5}{6}, \frac{7}{8}, \frac{11}{12}, \frac{3}{10}$
Answer$\frac{5}{6}, \frac{7}{8}, \frac{11}{12}, \frac{3}{10}$
L.C.M. of denominators $6,8,12,10=120$
| $2$ |
$6,$ |
$8,$ |
$12,$ |
$10$ |
| $2$ |
$3,$ |
$4,$ |
$6,$ |
$5$ |
| $3$ |
$3,$ |
$2,$ |
$3,$ |
$5$ |
| |
$1,$ |
$2,$ |
$1,$ |
$5$ |
$=2 \times 2 \times 3 \times 2 \times 5=120$
Now, $\frac{5}{6}=\frac{5 \times 20}{6 \times 20}=\frac{100}{120}$;
$\frac{7}{8}=\frac{7 \times 15}{8 \times 15}=\frac{105}{120} ; \frac{11}{12}=\frac{11 \times 10}{12 \times 10} $
$=\frac{110}{120} ; \frac{3}{10}=\frac{3 \times 12}{10 \times 12}=\frac{36}{120}$
$\therefore \frac{5}{6}, \frac{7}{8}, \frac{11}{12}, \frac{3}{10}=\frac{100}{120}, \frac{105}{120}, \frac{110}{120}, \frac{36}{120}$ View full question & answer→Question 195 Marks
Change the following groups of fractions to like fractions:
$\frac{1}{3}, \frac{2}{5}, \frac{3}{4}, \frac{1}{6}$
Answer$\frac{1}{3}, \frac{2}{5}, \frac{3}{4}, \frac{1}{6}$
L.C.M. of denominators $3,5,4,6=60$
| $2$ |
$3,$ |
$5,$ |
$4,$ |
$6$ |
| $3$ |
$3,$ |
$5,$ |
$2,$ |
$3$ |
| |
$1,$ |
$5,$ |
$2,$ |
$1$ |
$=2 \times 3 \times 1 \times 5 \times 2 \times 1=60$
Now, $\frac{1}{3}=\frac{1 \times 20}{3 \times 20}=\frac{20}{60}$;
$\frac{2}{5}=\frac{2 \times 12}{5 \times 12}=\frac{24}{60} ; \frac{3}{4}=\frac{3 \times 15}{4 \times 15}=\frac{45}{60}$
$\frac{1}{6}=\frac{1 \times 10}{6 \times 10}=\frac{10}{60} $
$\frac{1}{3}, \frac{2}{5}, \frac{3}{4} \text { and } \frac{1}{6}=\frac{20}{60}, \frac{24}{60}, \frac{45}{60}, \frac{10}{60}$ View full question & answer→