Page 96 - ICSE Math 7

1 1 1
Example 10: Divide 230 kg mangoes among three friends X, Y and Z in the ratio : : .
2 3 8
Solution: Converting the given ratio into its simplest form.




1 1 1  1 × 24 :  1 × 24 :  1 × 24 (LCM of 2, 3, 8 = 24)
: : =



2 3 8  2   3   8 



= 12 : 8 : 3
 12  12
Share of X =   × 230 kg = × 230 kg = 120 kg
 12 83++  23
 8  8
Share of Y =   × 230 kg = × 230 kg = 80 kg
 12 83++  23
 3  3
Share of Z =  12 83++  × 230 kg = 23 × 230 kg = 30 kg


Example 11: In what ratio should we decrease 1,500 to get 800?
Final quantity 800 8
Solution: Multiplying ratio = = =
Original quantity 1,500 15
∴ Original quantity : Final quantity = 15 : 8
Thus, if 1,500 is decreased in the ratio 15 : 8, we will get 800.
EXERCISE 7.1

1. Akriti earns ` 55,000 per month and spends ` 25,000 per month. Find the ratio of:
(a) her income to her expenditure (b) her savings to her income
2. If a : b = 9 : 5 and b : c = 15 : 3, find a : c.
3. Express the following ratios in their simplest form.
1 1
(a) 33 : 99 (b) 2.5 : 3.5 (c) 4 : 2 (d) 20 paise : ` 1
2 4
2
2 7
(e) 1 5 (f) 3 months : 1 year (g) : 5 (h) :
:
3 9 7 21 3 8
4. Find the compound ratio of the following.
1 3
(a) 3 : 5 and 2 : 5 (b) 7 : 6 and 2 : 3 (c) : and 10 : 3
2 4
2 4 3 7 2 3 5 14
(d) : and : (e) : and :
3 9 5 15 15 7 8 27
5. Find the multiplying ratio which changes ` 36 to ` 50.
6. A school library had 1,500 books in the year 2011. In 2012, the number of books increased in
the ratio 1 : 2. In 2013, the number of books further increased in the ratio 2 : 5. Find the number
of books in the year 2013.
7. In what ratio should we increase 900 to get 1,200?
8. Divide 2,700 in the ratio: (a) 5 : 4 (b) 1 : 2 : 6
1 1
9. Distribute 220 marbles between Ria and Anusha in the ratio : .
6 5
10. A number is divided in the ratio 7 : 5. If the second part is 150, find the number.
11. Which ratio is the greater amongst the following?
1 1 1 2 2 1
(a) 6 : 7, 9 : 11 (b) 3 : , 2 : 9 (c) 1 : 1 , 1 : 1
2 3 2 3 3 4
12. Divide ` 3,600 between A, B and C so that A has thrice as much as B and B has half as much as C.

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