I have to spend 1/10 of my income on house rent, 1/10 of remainder on conveyance 1/3 of further remainder on children's education after which I have Rs. 648 left over. What is my income?

Rs. 1200

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Rs. 1400

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Rs. 1700

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None of these

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Solution

The correct option is A Rs. 1200
Let I have x rupees
$A f t e r s p e n d i n g \frac{1}{10} o f i t o n h o u s e r e n t I h a v e$ $\frac{9 x}{10}$

$N o w o u t o f \frac{9 x}{10} I s p e n t$ $\frac{1}{10} o f i t$ $i . e ., \frac{9 x}{100} o n c o n v e y a n c e s o r e m a i n d e r w i l l b e$
$\frac{9}{10} x - \frac{9}{100} x = \frac{81 x}{100}$
$F u r t h e r I s p e n t \frac{1}{3} o f$ $\frac{81 x}{100}$ $i . e . \frac{27 x}{100} i n t o c h i l d r e n s e d u c a t i o n n o w I h a v e$ $\frac{54 x}{100},$
$S o, \frac{54 x}{100} = 648, x = 1200$

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