Two number are in the ratio 1:2 ,If 7 is added to both , the new numbers are in the ratio3:5, the GREATEST NUMBER IS
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Given :
Two numbers are in ratio.
7 is added to both = 3 : 5.
Find :
Greatest number.
According to the question :
Let the numbers be ' a ' and ' b '
Ratio = 1 : 2
a / b = 1 / 2
☞ 2a = b ........ ( 1 st equation )
7 is added to both = 3 : 5
( a + 7 ) / ( b + 7 ) = 3 / 5
☞ 5 ( a + 7 ) = 3 ( b + 7 )
☞ 5a + 35 = 3b + 21
☞ 5a - 3b = 21 - 35
☞ 5a - 3b = -14 ......... ( 2 nd equation )
Substituting ' b ' value in 1 st equation :
2a = y.
☞ 5a - 3 ( 2a ) = -14
☞ 5a - 6a = -14
☞ a = 14.
substituting ' x ' value in 1 st equation :
2a = b
☞ 2 × 14
☞ 28.
Therefore the numbers are
14 and 28.
Greatest number = 28.
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