1. REDUCTION IN CONSUMPTION :- Suppose the price of a commodity increase by R% and expenditure on this commodity remains the same. Then,
Reduction % in consumption = $\left \{ \frac{R}{(100+R)}\times 100 \right \}$%
For eg. If the price of a commodity be raised by 20%, find by how much percent must a householder reduce his consumption of that commodity so as not to increase his exprnditure?
sol. Reduction % in consumption = $\left \{ \frac{R}{(100+R)}\times 100 \right \}$%
= $\left \{ \frac{20}{(100+20)}\times 100 \right \}$% {$\because $ R = 20}
= $\frac{20}{120}\times 100$ %
= $\frac{1}{6}\times 100$ %
= $\frac{50}{3}$ %
= $16\frac{2}{3}$ %
2. INCREASE IN CONSUMPTION :- Suppose the price of a commodity falls down by R% and expenditure on this commodity remains the same. Then,
Increase % in consumption = $\left \{ \frac{R}{(100-R)}\times 100 \right \}$%
For eg. If the price of wheat decrease by 10%, by how much percent must a householder increase its consumption, so as not to decrease expenditure in this item?
sol. Increase % in consumption = $\left \{ \frac{R}{(100-R)}\times 100 \right \}$%
= $\left \{ \frac{10}{(100-10)}\times 100 \right \}$%
= $\left \{ \frac{10}{90}\times 100 \right \}$%
= $\frac{100}{9}$%
= $11\frac{1}{9}$%
3. FIRST INCREASE THEN DECREASE :- If the value of a number is first increased by x% and later decreased by x%, then the net change is always a decrease which is equal to,
x% of x or $\frac{x^{2}}{100}$.
NOTE :- In this case there is always a loss.
For eg. The salary of an employ is first increased by 10% and thereafter it was reduced by 10%. What was the change in his salary?
sol. by the above formula $\frac{x^{2}}{100}$%
decrease % = $\frac{(10)^{2}}{100}$%
= $\frac{100}{100}$%
= 1 %
Reduction % in consumption = $\left \{ \frac{R}{(100+R)}\times 100 \right \}$%
For eg. If the price of a commodity be raised by 20%, find by how much percent must a householder reduce his consumption of that commodity so as not to increase his exprnditure?
sol. Reduction % in consumption = $\left \{ \frac{R}{(100+R)}\times 100 \right \}$%
= $\left \{ \frac{20}{(100+20)}\times 100 \right \}$% {$\because $ R = 20}
= $\frac{20}{120}\times 100$ %
= $\frac{1}{6}\times 100$ %
= $\frac{50}{3}$ %
= $16\frac{2}{3}$ %
2. INCREASE IN CONSUMPTION :- Suppose the price of a commodity falls down by R% and expenditure on this commodity remains the same. Then,
Increase % in consumption = $\left \{ \frac{R}{(100-R)}\times 100 \right \}$%
For eg. If the price of wheat decrease by 10%, by how much percent must a householder increase its consumption, so as not to decrease expenditure in this item?
sol. Increase % in consumption = $\left \{ \frac{R}{(100-R)}\times 100 \right \}$%
= $\left \{ \frac{10}{(100-10)}\times 100 \right \}$%
= $\left \{ \frac{10}{90}\times 100 \right \}$%
= $\frac{100}{9}$%
= $11\frac{1}{9}$%
3. FIRST INCREASE THEN DECREASE :- If the value of a number is first increased by x% and later decreased by x%, then the net change is always a decrease which is equal to,
x% of x or $\frac{x^{2}}{100}$.
NOTE :- In this case there is always a loss.
For eg. The salary of an employ is first increased by 10% and thereafter it was reduced by 10%. What was the change in his salary?
sol. by the above formula $\frac{x^{2}}{100}$%
decrease % = $\frac{(10)^{2}}{100}$%
= $\frac{100}{100}$%
= 1 %
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