Fractions in Disguise Class 8 Solutions

Yellow is 1-\frac34=\frac14=25\% of the mixture.

Each fifth is 100\%\div5=20\%. Therefore two-fifths is 2\times20\%=40\%.

(i) \frac35=60\%; (ii) \frac7{14}=50\%; (iii) \frac9{20}=45\%; (iv) \frac{72}{150}=48\%; (v) \frac13=33\frac13\%; (vi) \frac5{11}=45\frac5{11}\%\approx45.45\%.

\frac{15}{25}\times100=60\%. Choice (iv).

\frac{15}{80}\times100=18.75\%.

Comparing each marked position with the full start-to-finish segment gives A about 38%, B about 55%, C about 72%, and D about 93%.

(i) 50\%>5\%; (ii) \frac5{10}=50\%; (iii) \frac3{11}<61\%; (iv) 30\%<\frac13.

The amounts are (0.25\times120=30) g and (0.35\times95=33.25) g. Madhav ate 3.25 g more sugar.

For (100,200,50,80,10,35,287): 25% gives (25,50,12.5,20,2.5,8.75,71.75); 10% gives (10,20,5,8,1,3.5,28.7); 20% gives (20,40,10,16,2,7,57.4); 5% gives (5,10,2.5,4,0.5,1.75,14.35).

For (100,200,50,80,10,35,287), 40% gives (40,80,20,32,4,14,114.8). Using 15\%=10\%+5\% gives (15,30,7.5,12,1.5,5.25,43.05).

(50\%=\frac12=0.5), (100\%=1=1.0), (25\%=\frac14=0.25), (75\%=\frac34=0.75), (10\%=\frac1{10}=0.1), (1\%=\frac1{100}=0.01), (5\%=\frac1{20}=0.05), (43\%=\frac{43}{100}=0.43).

(80\%\times75=\frac45\times75=60). Zubin needs at least 60 marks.

Millet is \frac2{2+7}=\frac29=22.22\% of the mixture. In 500 mL, the exact amount is (500\times\frac29=111\frac19) mL, about 111.1 mL.

The total is (92\div0.4=230) km. The remaining 60% is (230-92=138) km.

The percentages are 40\%,70\%,100\%,120\%, respectively. The ₹6,000 sale is 20% above target.

₹7,800 is 156\%, and ₹9,550 is 191\%. The 150% and 210% sales are ₹7,500 and ₹10,500.

(90\%=\frac9{10}=0.9); (110\%=\frac{11}{10}=1.1); (200\%=2=2.0); (250\%=\frac52=2.5); (15\%=\frac3{20}=0.15); (173\%=\frac{173}{100}=1.73); (358\%=\frac{179}{50}=3.58); (28.9\%=\frac{289}{1000}=0.289); (305\%=\frac{61}{20}=3.05).

(i) 20% of 75 is 15, and 60 is 80% of 75. (ii) One tenth of 90 is 9, and half is 45. (iii) One fourth of 140 is 35, and three fourths is 105.

(i) 40; (ii) 40; (iii) 223.2; (iv) 56; (v) (0.01\times60=0.6) minute = 36 seconds; (vi) (0.7) kg.

(\frac34\times60=45) mL red paint.

(i) (<); (ii) (<); (iii) (<); (iv) (<); (v) (>); (vi) (>). For (vi), the values are 24 and 15.36.

(i) 140, 210, 280. (ii) 21.5, 2.15, 12.9. (iii) 27, 54, 300.

The answers are 1\%, (1.6), and (50).

Yes. 10% of a day is 2.4 hours or 144 minutes. 1% of a week is 1.68 hours or 100.8 minutes.

On day (n), it eats (n) of (n+1) units, or \frac{n}{n+1}\times100\%. The sequence begins 50%, 66.67%, 75%, and increases toward but never reaches 100%; day 99 is 99%.

At a constant work rate, five equal 20% sections take (5\times18=90) days. The assumption is necessary because changing worker count, weather, or crop density would break the proportional relationship.

Warm-up is 9 minutes, play is 72 minutes, and cool-down is 9 minutes.

(0.9\times8.2=7.38) billion people, using the chapter's approximate world population.

Scaling the number served does not change the proportions. Of 2 kg, rava is 0.8 kg, sugar is 0.8 kg, and ghee is 0.4 kg.

DEF: sugar 66%, milk solids 20%, badam 8%, chemicals 6%. Zacni: sugar 68%, milk solids 16%, badam 10%, chemicals 6%. Zacni has more badam; both have the same chemical proportion. Each row totals 100%.

Manufacturer: (253-230)/230\times100=10\%. Wholesaler: (300-253)/253\times100\approx18.58\%. Kishanlal: (430-300)/300\times100\approx43.33\%. A ₹36 notebook at 20% profit sells for ₹43.20. If ₹50 is 125% of a crayon box's cost, the cost was 50/1.25=₹40.

Rice cost ₹350 and sold for ₹300, so loss is 50/350\times100=14.29\%; calculating per kg gives the same rate. The vase sells for (82\%\times₹2650=₹2173).

₹80 is 88% of the strawberry cost, so CP (=80/0.88\approx₹90.91) per kg. The cooker sells for (65\%\times₹1800=₹1170). Against ₹900 cost, profit is ₹270, or 30%.

The bill is correct: subtotal ₹450, CGST 9% = ₹40.50, SGST 9% = ₹40.50, total ₹531. Kishanlal's gross profit is ₹32,000 and net profit ₹24,000; Manisha's net profit margin on ₹1,50,000 revenue is 30%.

(1) 35/75\times100=46.67\% profit. (2) ₹712.50. (3) Profit is 25% of ₹2.5 crore = ₹0.625 crore, so expenditure is ₹1.875 crore. (4) ₹225. (5) 40/60\times100=66.67\%, choice (iv).

Car original price (=₹440000/0.85\approx₹5,17,647.06). Winner: 31.25% and at least 4 candidates. Inflation: 4/38\times100\approx10.53\%. Original number: 75. Buffaloes: overall loss about ₹5,079.37 or 3.08%. Elephants: (p\times1.05), choice (iv). Cameras: demand now is 15% of before, choice (iii).

Without compounding: ₹24,000. With annual compounding: ₹20,000 × 1.1² = ₹24,200, which is ₹200 more.

Without compounding: ₹24,000. With compounding: ₹20,000 × 1.05⁴ = ₹24,310.13 approximately. Both this and the previous simple-interest case gain 20% overall, but compounding adds interest on earlier interest.

If rate (r) is written as a decimal, simple interest is (prt). Compound interest is (p(1+r)^t-p). Corresponding total amounts are (p(1+rt)) and (p(1+r)^t).

Jasmine's total amount is (p+(p\times0.06\times4)), choice (vii). At 7% for 3 years, ₹50,000 earns ₹10,500 simple interest. Compounding gives ₹61,252.15 total, or ₹11,252.15 interest, ₹752.15 more.

Giridhar pays ₹12,500 × 0.12 × 3 = ₹4,500 interest. Raghava pays ₹12,500 × 1.1³ − ₹12,500 = ₹4,137.50. Giridhar pays ₹362.50 more.

Without compounding it takes 10 years. With annual compounding, (1.1^7<2) but (1.1^8>2), so it first doubles during year 8. Compound growth is exponential; simple growth is linear.

City: (1.5\times1.03^3=1.6390905) crore, about 1.64 crore. Bacteria: (506000\times1.025^2=531616.25), about 531,616 bacteria.

TV: (₹21000\times0.95=₹19,950). Village: (1250\times0.9^3=911.25), so about 911 people, or roughly 910 after sensible rounding.

Option A gains ₹200, a 200% gain; B gains ₹500, a 50% gain. Choose A for percentage return or B for absolute money. For purchases ₹180, ₹225, ₹300, choose ₹50, ₹50, and 20% (₹60), respectively.

On ₹200, successive discounts give ₹200 × 0.7 × 0.8 = ₹112, an effective 44% discount. A direct 50% discount gives ₹100, so Cakify is cheaper.

The final factor is (1.5\times0.5=0.75), a 25% loss. A ₹12,000 sale corresponds to ₹16,000 cost, so loss is ₹4,000. Break-even discount is 1-1/1.5=33\frac13\%. If Ariba has 120% of Arun's marbles, Arun has 100/120=83\frac13\% of Ariba's.

Bengaluru: (250\%\times50=125) lakh = 1.25 crore. Approximate shares: Germany 1%, India 18%, Bangladesh 2%, USA 4%. Mobile final price is (₹8250\times1.18=₹9735); choices (v) and (vi).

Mice: (p\times1.05\times0.98\times0.97=0.99813p), so statements (ii) and (vi) are true. Shop: final factor (1.35\times0.70=0.945), so the shopkeeper makes a 5.5% loss.

The outer square is (8\times8=64) grid-square units. E is half of a (4\times4) square, so its area is 8 units. Thus E occupies 8/64\times100=12.5\%.

They are always equal because (x\%\text{ of }y=\frac{x}{100}y=\frac{y}{100}x=y\%\text{ of }x). The three pairs evaluate to 2, 3, and 9 on both sides.

They are 40\%\times60\%=24\% of all students. Applied to 160, this gives 38.4. Since a headcount must be whole, the stated percentages cannot both be exact for a group of 160; an actual count would need clarified or rounded data.

Pencils: SP per pencil is (5/3) of CP, a 66\frac23\% profit. Bus fares: (1.03\times1.04=1.0712), a 7.12% increase. Breadth factor is (1/1.1=10/11), so it decreases exactly 1/11=9\frac1{11}\%.

Potato 70% = 45.5 g; vegetable oil 24% = 15.6 g; salt 3% = 1.95 g; spices 3% = 1.95 g.

Effective prices: A ₹50, B ₹66.67, C ₹75, so A, B, C from cheapest to costliest. Discounts are 50%, 33.33%, and 25%. For exactly 4 items, A costs ₹200; B and C each cost ₹300, so choose A.

If (x) leave, ((99-x)/(100-x)=0.98). Solving gives (x=50). Then 49 of the remaining 50 are left-handed.

Statements (i), (ii), and (v) are supported. Twenties lead both gender series; the female percentages are below the male percentages in every shown age group; and both senior values are below 10%. The graph does not show population counts, over 25% in the thirties for both groups, or 50% in the twenties.

Place all eight knights on squares of one colour, for example a1, c1, e1, g1, b2, d2, f2, h2. Every knight move lands on the opposite colour, so no two of these knights attack each other.