Proportional Reasoning-2 Class 8 Solutions

Yes, if the other ingredients and cooking are alike. Both simplify to 2:1, and cross-products agree: 6\times2=3\times4=12.

It means 1 cm on the map represents 60,00,000 cm on the ground. Since 1\text{ km}=100{,}000\text{ cm}, 60{,}00{,}000\text{ cm}=60\text{ km}.

Measure each straight map segment in centimetres and multiply by 60\text{ km/cm}. Depending on ruler placement and print scaling, the map gives roughly 290 km from Bengaluru to Chennai and 590 km from Mangaluru to Chennai. These are geographical, not road, distances.

After converting each measurement with its own scale, results should be close. Small differences come from print scaling, line thickness, ruler placement, projection, and rounding. At 1:50, divide every actual classroom length by 50 using the same units, draw the boundary, and place each object at its correspondingly scaled location.

Two chillies are half of four, so halve every term: 4 spoons coriander, 2 chillies, 1 spoon toor dal, and 1/2 spoon fenugreek. The ratio is 4:2:1:0.5.

Five parts equal 10 L, so one part is 2 L. Red is 4 L, blue is 6 L, and white is 10 L. Total volume is 4+6+10=20 L.

Scale every term by 3: cement 3 bags, sand 4.5 bags, and gravel 9 bags. Total mixture is 3+4.5+9=16.5 bag-equivalents.

The ratio has 3+4+3+5=15 parts, so each part is 10 minutes. Warm-up/cool-down takes 30 minutes, batting 40, bowling 30, and fielding 50.

Three parts equal 288, so one part is 96. The library has 2\times96=192 Hindi books and 96 English books.

The 10 ratio parts give counts 40, 30, 20, and 10. Their values total 40(10)+30(5)+20(2)+10(1)=₹600.

Choose any scale k>0 and construct sides 3k,4k,5k; the triangle is right-angled. All such triangles are similar, but they are congruent only when they use the same k, because different scale factors give different side lengths.

No. The two shorter sides would total 1+3=4 parts, which is less than 5 parts. This violates the triangle inequality.

The HCF is 2, so the ratio is 6:5:4:3:2, totalling 20 parts. Each part is 360^\circ/20=18^\circ. Thus A, B, C, D, E have angles 108^\circ,90^\circ,72^\circ,54^\circ,36^\circ.

Winter has 360-90-120=150 people. Since the total count equals 360, the sector angles are numerically the same: summer 90^\circ, rainy 120^\circ, winter 150^\circ.

Multiply each percentage by 360^\circ: Entertainment 180^\circ, Sports 90^\circ, News 54^\circ, and Information 36^\circ.

Let the collected counts be n_1,\ldots,n_7, with total N. For each subject draw a sector of angle (n_i/N)\times360^\circ. The angles must total 360^\circ; label each sector with its subject and count or percentage.

This is direct proportion: x=18{,}000\times5/4{,}500=20. Therefore 20 workers are needed, assuming equal productivity.

Speed and time are inversely proportional for fixed distance. Thus 30\times3=60t, giving t=1.5 hours.

Every product is 90: 5\times18=15\times6=30\times3=60\times1.5=90. Multiplying speed by 3, 2, or 2 divides time by the same factor, confirming inverse proportion.

1.5/18=1/12=0.08333\ldots, and 5/60=1/12. They are equal, as inverse proportion requires.

Tables (i) and (iii). In (i), every product is 800. In (iii), every product is 450. Table (ii) has products 800, 800, 312.5, and 128, so it is not inverse proportion.

The constant product is 16\times9=144. Therefore the missing entries are y=144/12=12, x=144/48=3, and y=144/36=4.

Their hourly rates are 1 and 2/3 jobs, so together they do 5/3 jobs per hour. One job takes 1/(5/3)=3/5 hour, or 36 minutes. At a fixed combined rate, work completed is directly proportional to time.

Pairs (i), (ii), and (iv): taps versus filling time, painters versus days for a fixed wall, and speed versus time for a fixed route. Pairs (iii), (v), and (vi) are direct under the stated fixed-rate assumptions.

At a fixed unit price, one pencil costs ₹5. Therefore 20 pencils cost 20\times₹5=₹100.

With equal daily use per family and no replenishment or wastage, family-days stay constant: 20\times6=30d. Hence d=4 days.

Reading the purple portion as sleep time out of 24 hours, from top-left to bottom-right the values are 2.5, 3.5, 8, 10.5, 13, 15, 18, and 20 hours.

Bus is most common at 120^\circ. Car is the remaining 30^\circ, or 1/12 of the children. If 18 travel by car, the total is 18\times12=216; the 60^\circ two-wheeler sector represents 36 children. Cycle and two-wheeler have equal 60^\circ sectors. The question says “taxis,” but the chart labels that sector “Two-wheeler.”

Total work is 3\times4=12 worker-days. Four equally productive workers need 12/4=3 days, assuming equal rates, full attendance, and no interference between workers.

At a fixed pump rate, time is directly proportional to tank count: 6\times5/2=15 hours.

There are 25\times12=300 chairs. At 20 chairs per row, 300/20=15 rows are needed.

Teaching time is 8\times45=360 minutes. Dividing by 9 gives 360/9=40 minutes per period.

The rates are 1/3 and 1/2 tank per hour, totalling 5/6. Time is 1/(5/6)=6/5 hour, or 1 hour 12 minutes.

Machine-days are fixed: 42\times63=m\times54. Thus m=49 machines, assuming identical machines and constant operating time and output.

The distance is fixed at 60\times2=120 km. At 80 km/h, time is 120/80=1.5 hours.