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ICSE Class X Notes 2025 : Mathematics (Carmel School, Jorhat)

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Yash Bajaj
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Selected Questions of Ratio & Proportion 1. Given 3 5 3 5 = , prove that 3 +5 = 3 +5 2. Two numbers are in the ratio of 3: 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers. 3. If a: b=5:3, find (5a + 8b) : (6a 7b). 4. If 3 +4 3 +4 3 4 = 3 4 , prove that = 5. The work done by (x - 3) men in (2x + 1) days and the work done by (2x + 1) men in (x+4) days are in the ratio of 3:10. Find the value of x. 6. What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion? 7. What number must be added to each of the numbers 6, 15, 20 and 43 to make them in proportion? 3 +5 7 8. If 3 5 = 3 , find x : y. 9. If = 10. If +3 + 3 , prove that 3 2 2 + 3 = 0 +3 3 8 5 8 +5 8 5 = 8 +5 , prove that = 11. What least number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion? 12. Given that 3 +3ab 3 +3a b proportion , prove that 63 = 62 using componendo and dividendo, find a : b. 13. If x, y, z are in continued ( + )2 ( + )2 2 + 2 + 2 2 14. Given, = 2 15.If 3 +4+ 3 5 + 2 2 2 = 2a x , use componendo and dividendo to prove that b = x + 1 = 9, using properties of proportion find x. 3 +4 3 5 16. 6 is the mean proportional between two numbers x and y and 48 is the third proportional of x and y. Find the numbers. 17. If = +1+ 1 +1 1 , prove that 2 2 + 1 = 0 18. Using the properties of proportion, solve for x, given 19. Given, 20. If = 3 +12a 6a2 +8 4 +1 17 2 2 =18 3 +27 = 9 2+27 ,find a:b 2 +1+ 2 1 2 +1 2 1 , prove that 2 4 + 1 = 0 21. If (3a+2b) : (5a+3b) =18: 29 , find a:b. 22. If 23. If 24. If 2 +2x 2x+4 = 2 +3 3 +9 2 + 4 2 1 2 4 2 1 5 + 2 6 5 + 2 6 , using properties of proportion find x:y. = 4 , using properties of proportion find x. = 4 , using properties of proportion find x. 25. The following numbers, K + 3, K + 2, 3K 7 and 2K - 3 are in proportion. Find K. 26. If (x -9): (3x + 6) is the duplicate ratio of 4 : 9, find the value of x using properties of proportion. *******************************************************************************

 

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