Question

Q23
A boys and 3 girls spent Rs. 120 on
the average, of which boys spend
Rs. 150 on the average, then the
average amount spent by girls is
O
Rs. 80
ORs. 60
ORs. 90
o Rs. 100​

Answer 1

$\textbf{Given:}$

$\textsf{Number of boys=4}$

$\textsf{Number of girls=3}$

$\textsf{Average amount spent by boys=Rs.150}$

$\textbf{To find:}$

$\textsf{Average amount spent by girls}$

$\textbf{Solution:}$

$\textbf{Combined average formula:}$

$\boxed{\mathsf{\overline{x}=\dfrac{n_1\,\overline{x_1}+n_2\,\overline{x_2}}{n_1+n_2}}}$

$\textsf{Here}$

$\mathsf{n_1=4,\;n_2=3,\;\overline{x_1}=150,\;\overline{x}=120}$

$\mathsf{Using\;combined\;average\;formula}$

$\mathsf{\overline{x}=\dfrac{n_1\,\overline{x_1}+n_2\,\overline{x_2}}{n_1+n_2}}$

$\mathsf{120=\dfrac{4\,(150)+3\,\overline{x_2}}{4+3}}$

$\mathsf{120=\dfrac{600+3\,\overline{x_2}}{7}}$

$\mathsf{120{\times}7=600+3\,\overline{x_2}}$

$\mathsf{840=600+3\,\overline{x_2}}$

$\mathsf{840-600=3\,\overline{x_2}}$

$\mathsf{240=3\,\overline{x_2}}$

$\mathsf{\overline{x_2}=\dfrac{240}{3}}$

$\implies\boxed{\mathsf{\overline{x_2}=80}}$

$\textbf{Answer:}$

$\textsf{Average amount spent by girls is Rs. 80}$

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