RRB Assistant Loco Pilot and Technician Model Paper 8 with solutions

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Question : 3 of 75

Marks: +1, -0

Two numbers are in the ratio 3 : 4. If the sum of their squares is 900, the smaller number is

18
24
16
27

Solution:

{ { x }/ { y } ={ 3 }/ { 4 } }

∴

{ x = { 3 y }/ { 4 } }

{ x ^ { 2 } + y ^ { 2 } }

= 900

{ ( { 3 y }/{ 4 } ) ^ { 2 } + y ^ { 2 } }

= 900

{ { 9 y ^ { 2 } }/ { 16 } + y ^ { 2 } }

= 900

{ { 9 y ^ { 2 } } /{ 16 } + y^ { 2 } }

= 900

{ 25 y ^ { 2 } }

= 900 x 16
or,

y ^ { 2 } = { 900 × 16 } { 25 }

y = √ { { 900 × 16 } /{ 25 } }

=

{ 30 ×4 }/ { 5 }

= 24

x = { 3×24 } /{ 4 }

= 18

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