This document provides solutions to ratio and proportion problems along with explanations. Some key points: - The ratio of 4:9, 3:4, and 2:3 and 9:7 compounded is 2:21 - If ratio is 7:10 and difference is 105, the numbers are 245 and 350 - Given ratios of P:Q and P:R, the ratio of Q:R is 27:22 - Given ratio of X:Y and values of X^2Y + XY^2 and X^3 + Y^3, the ratio is 84:91 - Given ratios and one speed, the speed of the other train can be calculated - To make the ratios 19:

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2. What will be the ratio compounded of 4:9, duplicate ratio of 3:4, and triplicate ratio of 2:3 and 9:7? Multiply : 4* 9* 8* 9 =2592 multiply : 9*16*27*7 =27216 thus ratio is : 2592:27216 =2:21 answer

3. The ratio of two numbers is 7:10, their difference is 105, what are the numbers? The difference is 3, so it is 105, so : 105/3*10 = 350 and 105/3*7 = 245 thus numbers are 245 and 350 answer.

4. P,Q,R are 3 cities, the ratio of temperature of P,Q is 11:12, and P and R 9:8, what is the ratio of Q & R is ? P = 11 * 9 = 99 cross multiply P11 to R 8 = 88, cross multiply P 9 to Q 12, = 108 thus P:Q:R= 99:108:88 Q:R=108:88 = 27:22 answer

5. X:Y = 3:4, the value of X^2Y+XY^2:X^3+Y^3 9*4+3*16:27+64 36+48:91 84:91 answer

6. The ratio between speed of two trains is 7:8 and 2 nd train runs 400 KM in 5 hours, the speed of the 1 st train is ? 400 * 7/8 = 350 km in 5 hours, so in 1 hours = 70 km per hour.

7. The number which when subtracted from each of terms of ratio 19:31 reducing it to 1:4 is ? 1:4 can be written as 2:8 or 3:24 or 4:16 or 5:20 reduce 15 from 19 and 31, it gives 4: 16, or 1:4 answer

8. A=B/2=C/5, then A:B:C is ? Product of denominators is 10 ( 2* 5 * 1 = 10) Let us assume C = 10, thus we can write : 2=4/2=10/5, or we can write : 2:4:10 or 1:2:5 as the ratio of A:B:C

9. If X/2=Y/3=Z/7, then the value of (2X-5Y+4Z) / 2Y X/2=Y/3=Z/7 = 1 X = 2, Y = 3, Z = 7 (2*2 – 5*3+4*7)/2*2 = =17/4 answer

10. The numbers 14,16,35,42 are not inproportion, 4 th term for which they will be in proportion is ? Instead of 42, write X. 14 X = 16* 35 X = 40

11. The value of 2*(256)^-1/8? 2 * ½ (when power is in negative, put the value as denominator) = 1 answer

12. (81X^4/Y^-8)^1/4 ? Power of 4 gets cancelled power of Y is – 8, so put Y as numerator and Y ^ 8, now divide 8 by 4, we get y^2 =81XY^2 answer

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