Set A Solutions

A1. Answer: (a) 1:1 C_1=7, C_2=9, M=8. Ratio =(9-8):(8-7)=1:1.

A2. Answer: (b) Rs 66 M = (60(3)+75(2))/(5) = (180+150)/(5)=(330)/(5)=66.

A3. Answer: (b) 5:1 Let CP of milk =1, water =0. Sold at CP of milk (SP =1) with 20% gain, so mean CP =(1)/(1.2)=(5)/(6). Milk : Water = (0-(5)/(6)):((5)/(6)-1) → magnitudes (5)/(6):(1)/(6) = 5:1.

A4. Answer: (c) 45 L Single withdrawal-replacement: 50-5=45 L (no repetition, so plain subtraction suffices — the general formula with n=1 gives the same: 50(1-5/50)^1=50(0.9)=45).

A5. Answer: (b) Rs 58 M=(6(50)+4(70))/(10)=(300+280)/(10)=(580)/(10)=58.

A6. Answer: (b) 2:1 C_1=20,C_2=50,M=30. Ratio =(50-30):(30-20)=20:10=2:1.

A7. Answer: (b) 5 L Milk =36 L, water =4 L. Let w L water be added: (4+w)/(40+w)=0.2 ⇒ 4+w=8+0.2w ⇒ 0.8w=4 ⇒ w=5.

A8. Answer: (b) 5:3 Vessel A milk fraction =(3)/(5)=0.6; Vessel B milk fraction =(1)/(3). Target fraction =(1)/(2). Ratio A:B =((1)/(2)-(1)/(3)):(0.6-(1)/(2)) = (1)/(6):(1)/(10). Multiply by 30: 5:3. Check: mix 5 parts of A (0.6 milk) and 3 parts of B ((1)/(3) milk): milk =5(0.6)+3((1)/(3))=3+1=4, total =8, fraction =0.5 ✓.

A9. Answer: (c) Rs 20.4 M=(20(18)+30(22))/(50)=(360+660)/(50)=(1020)/(50)=20.4.

A10. Answer: (b) 7:3 C_1=15,C_2=20,M=16.5. Ratio =(20-16.5):(16.5-15)=3.5:1.5=7:3.

A11. Answer: (c) 40 L Let milk =4x, water =x. After adding 10 L water: (4x)/(x+10)=2 ⇒ 4x=2x+20 ⇒ x=10. Milk =4x=40 L.

A12. Answer: (a) 1:2 Mean CP =(42)/(1.2)=35. C_1(Rs30), C_2(Rs45), M=35. Ratio (Rs30 : Rs45) = (45-35):(35-30)=10:5=2:1, so (Rs45 : Rs30) =1:2.

A13. Answer: (b) 72.9 L P=100,x=10,n=3. Milk left =100(0.9)^3=100(0.729)=72.9 L.

A14. Answer: (c) 22 L Milk =66×(5)/(6)=55 L, water =66×(1)/(6)=11 L. For ratio 5:3, water needed =55×(3)/(5)=33 L. Water to add =33-11=22 L.

A15. Answer: (a) 11:5 Equal volume, take each vessel =8 units (LCM-friendly). Vessel 1 (3:1, sum 4, scaled to 8): milk =6, water =2. Vessel 2 (5:3, sum 8): milk =5, water =3. Total milk =6+5=11, total water =2+3=5. Ratio =11:5.

A16. Answer: (a) 1:3 C_1=50, C_2=70, M=65. Ratio =(70-65):(65-50)=5:15=1:3.

A17. Answer: (c) Rs 52 M=(8(40)+12(60))/(20)=(320+720)/(20)=(1040)/(20)=52.

A18. Answer: (c) 54 L Single withdrawal, no repetition: 60-6=54 L.

A19. Answer: (b) 2:1 C_1=25, C_2=40, M=30. Ratio =(40-30):(30-25)=10:5=2:1.

A20. Answer: (c) 10 L Milk =30×(2)/(3)=20 L, water =10 L (fixed, since only water is added). For a 1:1 ratio, water must become 20 L, so 10 L must be added.