Question

Prema received a certain amount of money on her retirement for her employer. she gives half of this money and an additional sum of rupees 10,000 to her daughter. she also gives one third of the money received and an additional sum of rupees 3000 to her son. if the daughter gets twice as much as the son, find the amount of money Prema received on her retirement.

Answer 1

Answer:x = 24000

Step-by-step explanation:

money got by daughter = 2 x ( money got by son) 

x/2 + 10000 = 2(x/3 + 3000) 

x + 20000/2 = 2( x + 9000) /3) 

(x + 20000)/2 = (2x + 18000)/3 

3x + 60000 = 4x + 36000

x = 60000 - 36000

x = 24000

Answer 2

$\sf{\blue{\huge{Answer}}}$


$\sf{\green{Rs. \: 24000}}$


$\sf{\blue{\huge{Explanation}}}$

$\sf Let \: the \: amount \: o f\: Money \: received \: by \: Prema \: be \: x. \\ \sf Money \: given \: to \: her \: daughter =Rs. \bigg( \frac{x}{2} + 10000 \bigg) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= Rs. \bigg ( \frac{x + 20000}{2} \bigg) \\ \\ \sf Money \: given \: to \: her \: son = Rs. \bigg( \frac{x}{3} + 3000 \bigg) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= Rs. \bigg( \frac{x + 9000}{3} \bigg) \\ \sf By \: the \: Given \: condition \\ \sf \frac{x + 20000}{2} = 2 \bigg( \frac{x + 9000}{3} \bigg) \\ \implies \sf \frac{x + 20000}{2} = \frac{2x + 18000}{3} \\ \sf \implies3(x + 20000) = 2(2x + 18000) \\ \sf \implies3x + 60000 = 2x + 36000 \\ \sf \implies 60000 - 36000 = 4x - 3x \\ \sf \implies24000 = x \\ \\ \sf Amount \: of \: money \: received \: by \: Prema = \bf{ Rs.\: 24000}$