QuestionA 20% price drop in sugar allows buying 2 kg more for Rs. 80. Find the new price per kg: (a) Rs. 10 (b) Rs. 8 (c) Rs. 6 (d) Rs. 7 (e) None.

Studdy Solution

STEP 1

Assumptions1. The original price of sugar is unknown. . The price of sugar is reduced by20%.
3. After the reduction, a man can obtain kg more sugar for Rs.80.
4. We need to find the reduced price of sugar per kg.

STEP 2

Let's denote the original price of sugar per kg as. After a20% reduction, the new price per kg is80% of, or0.8.
$Reduced\, price =0.8$

STEP 3

Before the price reduction, the man could buy a certain amount of sugar for Rs.80. Let's denote this amount as A kg. Therefore, we have $80 = A \cdot$

STEP 4

After the price reduction, the man can buy2 kg more sugar for the same amount of Rs.80. Therefore, we have $80 = (A +2) \cdot0.8$

STEP 5

We now have two equations with two variables (A and). We can solve these equations simultaneously to find the values of A and.First, let's express from the first equation $=80 / A$

STEP 6

Now, substitute from the first equation into the second equation $80 = (A +2) \cdot0.8 \cdot (80 / A)$

STEP 7

implify the equation $80A =64A +128$

STEP 8

Subtract64A from both sides of the equation $16A =128$

STEP 9

olve for A $A =128 /16 =8$

STEP 10

Substitute A =8 into the first equation to find $=80 /8 =10$

STEP 11

The original price of sugar per kg is Rs.10. After a20% reduction, the new price per kg is $Reduced\, price =0.8 \cdot10 =8$ So, the reduced price of sugar per kg is Rs.8.

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QuestionA 20% price drop in sugar allows buying 2 kg more for Rs. 80. Find the new price per kg: (a) Rs. 10 (b) Rs. 8 (c) Rs. 6 (d) Rs. 7 (e) None.

Studdy Solution

STEP 1

Assumptions1. The original price of sugar is unknown. . The price of sugar is reduced by20%.
3. After the reduction, a man can obtain kg more sugar for Rs.80.
4. We need to find the reduced price of sugar per kg.

STEP 2

Let's denote the original price of sugar per kg as. After a20% reduction, the new price per kg is80% of, or0.8.
$Reduced\, price =0.8$

STEP 3

Before the price reduction, the man could buy a certain amount of sugar for Rs.80. Let's denote this amount as A kg. Therefore, we have $80 = A \cdot$

STEP 4

After the price reduction, the man can buy2 kg more sugar for the same amount of Rs.80. Therefore, we have $80 = (A +2) \cdot0.8$

STEP 5

We now have two equations with two variables (A and). We can solve these equations simultaneously to find the values of A and.First, let's express from the first equation $=80 / A$

STEP 6

Now, substitute from the first equation into the second equation $80 = (A +2) \cdot0.8 \cdot (80 / A)$

STEP 7

implify the equation $80A =64A +128$

STEP 8

Subtract64A from both sides of the equation $16A =128$

STEP 9

olve for A $A =128 /16 =8$

STEP 10

Substitute A =8 into the first equation to find $=80 /8 =10$

STEP 11

The original price of sugar per kg is Rs.10. After a20% reduction, the new price per kg is $Reduced\, price =0.8 \cdot10 =8$ So, the reduced price of sugar per kg is Rs.8.

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QuestionA 20% price drop in sugar allows buying 2 kg more for Rs. 80. Find the new price per kg: (a) Rs. 10 (b) Rs. 8 (c) Rs. 6 (d) Rs. 7 (e) None.

Studdy Solution

STEP 1

Assumptions1. The original price of sugar is unknown. . The price of sugar is reduced by20%.3. After the reduction, a man can obtain kg more sugar for Rs.80.4. We need to find the reduced price of sugar per kg.

STEP 2

Let's denote the original price of sugar per kg as. After a20% reduction, the new price per kg is80% of, or0.8.Reduced price=0.8Reduced\, price =0.8Reducedprice=0.8

STEP 3

Before the price reduction, the man could buy a certain amount of sugar for Rs.80. Let's denote this amount as A kg. Therefore, we have80=A⋅80 = A \cdot80=A⋅

STEP 4

After the price reduction, the man can buy2 kg more sugar for the same amount of Rs.80. Therefore, we have80=(A+2)⋅0.880 = (A +2) \cdot0.880=(A+2)⋅0.8

STEP 5

We now have two equations with two variables (A and). We can solve these equations simultaneously to find the values of A and.First, let's express from the first equation=80/A =80 / A=80/A

STEP 6

Now, substitute from the first equation into the second equation80=(A+2)⋅0.8⋅(80/A)80 = (A +2) \cdot0.8 \cdot (80 / A)80=(A+2)⋅0.8⋅(80/A)

STEP 7

implify the equation80A=64A+12880A =64A +12880A=64A+128

STEP 8

Subtract64A from both sides of the equation16A=12816A =12816A=128

STEP 9

olve for AA=128/16=8A =128 /16 =8A=128/16=8

STEP 10

Substitute A =8 into the first equation to find=80/8=10 =80 /8 =10=80/8=10

STEP 11

The original price of sugar per kg is Rs.10. After a20% reduction, the new price per kg isReduced price=0.8⋅10=8Reduced\, price =0.8 \cdot10 =8Reducedprice=0.8⋅10=8So, the reduced price of sugar per kg is Rs.8.

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Assumptions1. The original price of sugar is unknown. . The price of sugar is reduced by20%.
3. After the reduction, a man can obtain kg more sugar for Rs.80.
4. We need to find the reduced price of sugar per kg.

Let's denote the original price of sugar per kg as. After a20% reduction, the new price per kg is80% of, or0.8.
$Reduced\, price =0.8$

Before the price reduction, the man could buy a certain amount of sugar for Rs.80. Let's denote this amount as A kg. Therefore, we have $80 = A \cdot$

After the price reduction, the man can buy2 kg more sugar for the same amount of Rs.80. Therefore, we have $80 = (A +2) \cdot0.8$

We now have two equations with two variables (A and). We can solve these equations simultaneously to find the values of A and.First, let's express from the first equation $=80 / A$

Now, substitute from the first equation into the second equation $80 = (A +2) \cdot0.8 \cdot (80 / A)$

implify the equation $80A =64A +128$

Subtract64A from both sides of the equation $16A =128$

olve for A $A =128 /16 =8$

Substitute A =8 into the first equation to find $=80 /8 =10$

The original price of sugar per kg is Rs.10. After a20% reduction, the new price per kg is $Reduced\, price =0.8 \cdot10 =8$ So, the reduced price of sugar per kg is Rs.8.