Question

A toy was sold at a gain of 12% .Had it been sold for ₹ 33 more the gain would have been

14% . Find the C.P of the toy.​

Answer 1

Answer:

Answer is ₹1650

Step-by-step explanation:

Let the C P of the toy = Rs.1oo

If the gain is 12%, the first S P = 100 + 12 = Rs.112

If he had been sold Rs.33 more gain = 14 %

Therefore second S P = 100 = 14 = Rs 114 .

Difference in second S P and first S P = Rs.2 [ 114 - 112=2]

If Rs,2 is the difference in S P , cost price = Rs. 100

If the difference in S P is Rs.33, cost price =

100/2*33= 50 x 33 = Rs1650

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Answer 2

GɪᴠᴇN :-

• A toy was sold at a gain of 12 % .
• If it had been sold for ₹ 33 more the gain would have been 14% .

Tᴏ FɪɴD :-

• The CP of the toy .

AɴsᴡᴇR :-

Given that , a toy was sold at the gain of 12% . If it was sold for Rs 33 more then the gain would have been 14 %. So ,

$\underline{\red{\sf Let \ us \ take :-}}$

• $\sf CP \ of \ the \ toy \ be \ \bf{x} .$

$\large\underline{\underline{\blue{\sf \leadsto Case:1- When \ it \ is \ sold \ at \ gain \ of \ 12\% . }}}$

$\pink{\tt:\implies SP = CP\bigg\lgroup\dfrac{100+gain\%}{100}\bigg\rgroup }\\\\\tt:\implies SP = x \bigg\lgroup\dfrac{100+12}{100}\bigg\rgroup \\\\\tt:\implies SP = x \times \dfrac{112}{100} \\\\\boxed{\red{\hookrightarrow} \bf SP = 1.12 x }$

$\rule{200}2$

$\large\underline{\underline{\blue{\sf \leadsto Case:2- When \ it \ is \ sold \ at \ gain \ of \ 14\% . }}}$

$\pink{\tt:\implies SP = CP\bigg\lgroup\dfrac{100+gain\%}{100}\bigg\rgroup }\\\\\tt:\implies SP = x \bigg\lgroup\dfrac{100+14}{100}\bigg\rgroup \\\\\tt:\implies SP = x \times \dfrac{114}{100} \\\\\boxed{\red{\hookrightarrow} \bf SP = 1.14 x }$

$\rule{200}2$

$\underline{\underline{\orange{\boldsymbol{According \ to \ the \ Question :- }}}}$

$\tt:\implies SP_{(At\ 14\%\ gain )} - SP_{(At\ 12\%\ gain )} = Rs 33\\\\\tt:\implies 1.14x - 1.12x = Rs 33\\\\\tt:\implies 0.02x = Rs 33 \\\\\tt:\implies \dfrac{2}{100}x = Rs 33 \\\\\tt:\implies x =\dfrac{33\times 100}{2} \\\\\underline{\boxed{\red{\tt\longmapsto CP = Rs \ 1650 }}}$

$\boxed{\pink{\dag}\:\:\green{\bf Hence \ the \ cost \ price \ of \ the \ toy \ is \ Rs 1650. }}$